We provide understanding quadrilaterals practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on understanding quadrilaterals skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of understanding quadrilaterals Questions

Question NoQuestionsClass
1( A B C D ) is a square of side ( 14 mathrm{cm} . ) Find
8
2n an isosceles, trapezium ( A B C D, angle C )
is equal to:
45
155 5
3. ( 65^{circ} )
( c cdot 105 )
0.75
8
3Given: Parallelogram ( A B C D ) in which
diagonal ( A C ) and ( B D ) intersect at ( M )
Prove ( M ) is the mid-point of ( L N )
8
4In the figure, ABCDEF is a regular hexagon, and its centre is point 0. What
is the value of ( x ? )
A ( cdot 80^{circ} )
B. ( 60^{circ} )
( c cdot 40^{circ} )
( D .30 )
8
568. If ABCD is a cyclic parallelo-
gram, then the ZA is
(1) 100° (2) 60°
(3) 80º (4) 90°
8
6Draw two angles of ( 90^{circ} ) at the ends of a line segment. Extend these rays. Do you get a triangle. Join these 2 rays by another line segment which shape can yo get? What will be the measure of all the angles?8
7Define a polygon.8
8What is a regular polygon?8
9PQRS is a parallelogram whose diagonals intersect at ( mathrm{M} )
If ( angle P M S=54^{circ}, angle Q S R=25^{circ} ) and
( angle boldsymbol{S} boldsymbol{Q} boldsymbol{R}=boldsymbol{3} boldsymbol{0}^{circ}: ) find ( angle boldsymbol{R} boldsymbol{P} boldsymbol{S} )
A ( .86^{circ} )
B. ( 96^{circ} )
( c cdot 92^{circ} )
D. ( 100^{circ} )
8
1010. In the figure given below, PTU is a straight line.
What is the value of x?
(a) 100
@ 120d
(b) 110
) 130
8
11Find the number of sides of a regular
polygon if each exterior angle
measures: ( 60^{circ} )
8
12If diagonals of the parallelogram are equal,then show that it is a rectangle.8
13The bisector of any two adjacent angles of a square form an isosceles-rightangled triangle. If the above statement is true then
mention answer as 1 , else mention 0 if
false
8
14In a rectangle ( A B C D ), diagonals intersect
at ( 0 . ) If ( angle O A B=30^{circ} ) find: ( angle A C B, angle A B O, angle )
( mathrm{COD}, angle mathrm{BOC} )
8
157.
Construct a rhombus PAIR, given that PA=6 cm and angle
ZA=110°.
8
16In a parallelogram ( A B C D, ) if ( A B= ) ( mathbf{2} boldsymbol{x}+mathbf{5}, boldsymbol{C} boldsymbol{D}=boldsymbol{y}+mathbf{1}, boldsymbol{A} boldsymbol{D}=boldsymbol{y}+mathbf{5} ) and
( B C=3 x-4, ) what is the ratio of ( A B )
and ( B C ? )
A .71: 21
B. 12: 11
c. 31: 35
D. 4: 7
8
17In parallelogram ( A B C D ) the length ( A B )
and ( C D ) are both 4 , the length of
diagonal ( A C=4 ) and the length of
diagonal ( B D=6 . ) The length ( A D ) equal
to
A. ( sqrt{10} )
B. ( sqrt{12} )
( c cdot sqrt{15} )
D. ( sqrt{20} )
8
181.
In Fig., AB || DC. Find the value of x.
8
19A regular polygon is inscribed in a
circle. If a side subtends an angle of ( 30^{circ} )
at the centre, what is the number of its
sides?
A . 10
B. 8
( c .6 )
D. 12
8
2011. A lilne lis parallel to line m and a transversal p interesects
them at X, Y respectively. Bisectors of interior angles at
X and Y intersect at P and Q. Is PXQY a rectangle? Give
reason.
8
21HOPE is a parallelogram as shown in
the given figure. The value of ( y ) is
( mathbf{A} cdot 21^{circ} )
B . ( 14^{circ} )
( c cdot 35^{circ} )
( D cdot 27 )
8
22One angle of a six-sided polygon is ( 140^{circ} )
and the other angles are equal. Find the measure of each equal angle.
( mathbf{A} cdot 116^{circ} )
B . ( 130^{circ} )
c. ( 120^{circ} )
D. ( 110^{circ} )
8
2311.
The diagonals of a quadrilateral are of lengths 6 cm and
8 cm. If the diagonals bisect each other at right angles,
what is the length of each side of the quadrilateral ?
8
24The angles of a convex pentagon are in
the ratio ( 2: 3: 5: 9: 11 . ) Find the
measure of each angle.
8
255.
In which quadrilateral digonals bisect each other?
(a) Parallelogram
(b) Rectangle
(c) Square
(d) Rhombus
8
26In a parallelogram ( A B C D, ) the side ( D C )
is produced to ( E ) and ( angle B C E=105^{circ} )
Calculate ( angle A, angle B, angle C, ) and ( angle D )
8
27In the figure given below, ( A B C D ) is a
trapezium in which ( A B | D C . E ) and ( F )
are the midpoint of ( A D ) and ( B C )
respectively. ( D F ) and ( A B ) are produced
to meet at ( G . ) Also ( A C ) and ( E F ) intersect
at point ( O . ) Show that :
( (i) E O | A B )
( (i) A O=C O )
8
28Say True or False. All the sides of a rhombus are of equal
length.
A. True
B. False
8
29Assertion : A polygon bounded by four line segments is
Reason: A polygon bounded by seven line segments is
called a hexagon
Assertion : Anolygon having 16 sides is nolled 16
8
3012. ABCD is a parallelogram. Points P and Q are taken on the
sides AB and AD respectively and the parallelogram PRQA
is formed. If ZC=45°, find ZR
8
31Two angles of a hexagon are ( 90^{circ} ) and
( 10^{circ} ) remaining four angles are equal find each equal angle.
8
32Classify the following curve as open or
closed:
8
33If in a polygon the number of diagonals
is 54 then the number of sides of this
polygon is?
8
34Two angles of a polygon are right
angles and the remaining are ( 120^{circ} )
each. Find the number of sides in it.
8
35(a) Is it possible to have a regular polygon with measure of each exterior
angle as ( 22^{circ} ? )
(b) Can it be an interior angle of a regular polygon? Why?
8
36In the given figure ( overrightarrow{A B} | overrightarrow{D E} ) and area
of the parallelogram ABFD is ( 24 c m^{2} )
Find the area of ( Delta A F B )
8
37In the rhombus ( A B C D, A C ) and ( B D ) are the diagonals. If the diagonals are ( 16 mathrm{cm} ) and ( 12 mathrm{cm} . ) Find the length of each of its sides.
( A cdot 10 mathrm{cm} )
B. 12 ( mathrm{cm} )
( c cdot 9 mathrm{cm} )
D. ( 8 mathrm{cm} )
8
389.
Find the values of x and y in the following parallelogram.
by
Find
120 (5x + 1000
8
395.
Is it possible to construct a quadrilateral ROAM in which
RO= 4 cm, OA=5 cm, 20= 120°, ZR= 105º and ZA=
135°? If not, why?
8
40( A B ) and ( C D ) are two vertical poles of
height ( 6 m ) and ( 11 m ) respectively. If the
distance between their feet is ( 12 m, ) find
the distance between their tops.
( mathbf{A} cdot 13 m )
B. ( 5 m )
( c .11 m )
D. ( 12 m )
8
41If the points ( boldsymbol{P}(mathbf{2}, mathbf{1},-mathbf{3}), boldsymbol{Q}(mathbf{5}, mathbf{4}, mathbf{3}) ) and
( R(1,4,7) ) are three vertices of a parallelogram ( P Q R S ) then the other
vertex is
A. (1,0,0)
В . (-2,1,1)
c. (-2,2,1)
D. (2,1,2)
8
42If the diagonal of a rectangle is twice one of the sides, then the ratio of the
sides of the rectangle is
A. ( sqrt{2}: 1 )
в. ( sqrt{3}: 1 )
( c cdot 2 sqrt{2}: 1 )
D. ( 2 sqrt{3}: 1 )
8
43In a parallelogram PQRS, X is the mid
point of PS and Y is the mid point of QR, then ( X Y ) divides ( Q S ) in the ratio of
A .1: 4
B. 1: 1
c. 1: 2
D. 1: 3
8
B. It is a polygon
c. It is an octagon
D. It is a regular polygon
8
45One angle of a seven-sided polygon is
( 114 . ) and each of the other six angles is ( x )
( 0^{0} ) The value of ( x ) is
A ( .114^{circ} )
B . ( 121^{circ} )
( c cdot 131^{0} )
D. ( 151^{circ} )
8
4616.
Study the figure and answer the following questions.
(1) Name a pair of adjacent sides.
(ii) How many pairs of opposite sides are these ?
(iii) How many pairs of adjacent angles are there?
(iv) Name a pair of opposite angles ?
(V) How many pairs of opposite angles are there?
17
Thaadionant fimira DORS is a trapezium in which SRIPO
8
47Give Reason:
A square can be thought of as a special rectangle.
8
48Two times the interior angle of a regular polygon is equal to seven times is exterior angle. Find the interior angle of
the polygon and the number of sides in ¡t.
A. ( 130^{circ} ) and ( n=9 )
B. ( 140^{circ} ) and ( n=9 )
c. ( 160^{circ} ) and ( n=9 )
D. ( 170^{circ} ) and ( n=9 )
8
49( P Q R S ) is a parallelogram. From the
information given in the figure, find the
values of ( x ) and ( y )
8
506.
A mason has made a concrete slab. He needs it to be
rectangular. In what way(s) can he make sure that it is
rectangular?
(a) By measuring each angle
(b) By making opposite sides parallel
(c) By measuring the lengths of the diagonals
(d) All of these
8
51A curve which has 2 end points is called
an
A. closed curve
B. simple curve
c. open curve
D. None of the above
8
52( P R ) and ( Q S ) are two diameters of a
circle with center ( O ) such that
( angle P O Q=90 . ) Then the quadrilateral
PQRS is a
A. rectangle
( c . ) rhombus
D. square
8
53Area of a rhombus if its vertices are ( (3, )
0), (4,5),(-1,4) and (-2,-1) taken in order
is
A . 24. sq. units
B. 36 sq. units
c. 48 sq. units
D. ( 48 sqrt{2} ) sq. units
8
54Find the sum of exterior angles ( boldsymbol{x}+boldsymbol{y}+ )
( boldsymbol{z}+boldsymbol{p}+boldsymbol{q} )
8
if
A. opposite angles are equal.
B. opposite angles aren’t obtuse, neither acute.
c. opposite sides are not equal.
D. none
8
56PQRS is a parallelogram and diagonals PR and ( \$ Q ) bisect at ( 0 . ) If ( P O=3.5 mathrm{cm} ) and
( 0 Q=4.1 mathrm{cm} . ) What is the length of the
diagonals?
8
5717. () What is the minimum interior angle possible for a
regular polygon? Why?
(i) What is the maximum exterior angle possible for a
regular polygon?
8
58In a parallelogram ( A B C D, ) if ( A B=2 x+5 ) ( mathrm{CD}=mathrm{y}+1, mathrm{AD}=mathrm{y}+5 ) and ( mathrm{BC}=3 mathrm{x}-4 ) then the
ratio of AB:BC is
A . 71:21
B. 12:11
( c cdot 31: 35 )
D. 4: 7
8
59If ( A B C D ) is parallelogram. E is mid-point of ( A B ) and ( C E ) bisects ( angle B C D, ) then
( angle D E C ) is
A ( cdot 60^{circ} )
В. ( 90^{circ} )
( c cdot 100^{circ} )
D. 120
8
60If the figure PQRS is a square M is the midpoint of PQ & RM ( perp ) AB. Prove that
( mathrm{RA}=mathrm{RB} )
8
611.
The ratio between exterior angle and interior angle of
regular polygon is 1:5. Find the number of sides of the
polygon
8
62A rectangle ( P Q R S ) is inscribed in a
quadrant of a circle, with ( P ) at the
centre and ( R ) on the circumference. If
( P S ) is ( 12 mathrm{cm} ) and ( Q P ) is ( 5 mathrm{cm} ) then the
diameter of the circle is
( mathbf{A} cdot 26 mathrm{cm} )
B. ( 29 mathrm{cm} )
( mathbf{c} .28 mathrm{cm} )
D. none of these
8
63The interior of a closed figure has a
A. space
B. boundary
c. diagonal
D. None of the above
8
64In a trapezium ( A B C D ) with ( A B | C D )
the given that ( A D ) is not parallel to ( B C ) Is ( triangle A B C cong triangle A D C ? ) Give reasons
8
65To find the sum of interior angles, we
multiply the number of triangles by
( mathbf{A} cdot 360^{circ} )
B. ( 120^{circ} )
( c cdot 180^{circ} )
D. ( 240^{circ} )
8
66( A B C D ) is a rhombus such that
( angle A D B=50^{circ}, ) then what is the
measure of ( angle A C B ? )
8
67Find the sum of exterior angles obtained on producing, in order, the sides of a polygon with:
(i) 7 sides
(ii) 10 sides
(iii) 250 sides
8
688.
The diagonals of a rectangle bisect each other at right
angles.
ana hisect each other at right angles.
8
69Is it possible to have a regular polygon
whose each interior angle is ( 170^{circ} )
State true or false:
A. True
B. False
8
70What is a regular polygon? State the name of a regular polygon of
(i) 3 sides
(ii) 4 sides
(iii) 6 sides
8
711.
The ratio of two sides of a parallelogram is 4 : 3 and its
perimeter is 56 m. If the sides of parallelogram be a and b.
atb
Then
is
8
72The perimeter of a parallelogram,whose one side measures 12 inches, is 72 inches. Find the length of its other three sides.
A. 12,12,36
B. 12, 18, 18
c. 12,24,24
D. 12,30,30
8
733.
Some rectangles are also squares.
8
74Sum of interior angle of quadrilateral
equals
A . ( 300^{circ} )
B. ( 180^{circ} )
( c .360^{circ} )
D. ( 540^{circ} )
8
75Fill in the blank
All squares are (similar,
congruent)
A. similar
B. congruent
c. Undefined
D. None of these
8
763.
The bisectors of angles of a parallelogram enclose a
S
(a) Rhombus
(c) Square
(b) Rectangle
(d) Parallelogram
TI
8
77There is a regular polygon whose each
interior angle is ( 145^{circ} ) State true or false.
A. True
B. False
8
78The straight line ( A B ) is divided at ( C ) so that ( A C=3 C B . ) Circles are described
on ( A C ) and ( C B ) as diameters and a
common tangent meets AB produced at
D. Then ( B D ) equals.
A. the diameter of the smaller circle
B. the radius of the smaller circle
c. the radius of the larger circle
D. ( overline{C B} sqrt{3} )
E. the difference of the two radi
8
79How many diagonals are there in a
hexagon?
A. 6
B. 4
( c cdot 11 )
( D )
8
80State true or false.
Is it possible to have a regular polygon
whose each exterior angle is ( 32^{circ} )
A. True
B. False
8
81In a rectangle ( A B C D, A B=12 mathrm{cm} )
and ( angle B A C=30^{circ} . ) Calculate the length
of side ( B C ) and diagonal ( A C )
8
82ABCD is a rhombus whose one angle is 60′. The ratio
the lengths of its diagonals is
(a) 3:1
(b) 2:1
(c) 2:1
(d) 3:1
8
83Examine the table.
(Each figure is divided into triangles
and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with number of sides?
(a) ( 7(b) 8 )
( (c) 10(d) n )

8
84In a trapezium ( A B C D, ) side ( A B ) is parallel to side ( mathrm{DC} ; ) and the diagonals ( mathrm{AC} ) and ( mathrm{BD} )
intersect each other at a point
Such that:
( boldsymbol{P A} times boldsymbol{P D}=boldsymbol{P B} times boldsymbol{P C} )
A. True
B. False
8
852.
In Fig, find the measure of ZMPN.
OU
M
8
86Find the number of diagonals of a
polygon of 16 sides.
8
87In the adjoining figure, ( A B C D ) is a
trapezium in which ( A B )

DC and ( A D=B C . ) If ( P, Q, R, S ) be
respectively the midpoints of ( B A, B D ) and ( C D, C A ) then show that
PQRS is a rhombus.

8
88The diagonals of a rectangle ( A B C D )
intersect each other in ( O . ) If angle ( A O D )
is ( 30^{0}, ) then find angle ( O C D )
8
891.
How many diagonals does each of the following have?
( A convex quadrilateral (ii) A regular hexagon
(i) A triangle
8
90What is a curve?
A. A line which is not straight and does not any sharp edges
B. It is a polygon
C . It is a quadrilateral
D. A line with sharp edges.
8
9113. In the following figure, FD || BC || AE and AC || ED. Find the
value of x.
5640
n
.
1
8
92Classify the given curves are (i) Open or
(ii) Closed.
8
93How many sides does a regular polygon
has if each of it’s interior angle is ( 120^{circ} ? )
8
94State true or false:
Is it possible to have a polygon whose
sum of interior angles is ( 540^{circ} ? )
A. True
B. False
8
95ABCD is a trapezium in which ( boldsymbol{A B} | ) ( boldsymbol{D} boldsymbol{C}, boldsymbol{A B}=mathbf{5 0} mathrm{cm}, boldsymbol{D} boldsymbol{C}=mathbf{3 0} mathrm{cm} . ) If ( boldsymbol{X} )
and ( Y ) are respectively the mid-points
of ( A D ) and ( B C, ) prove that
( boldsymbol{a} boldsymbol{r}(operatorname{trap} cdot boldsymbol{D} boldsymbol{C} boldsymbol{Y} boldsymbol{X})= )
( frac{mathbf{7}}{mathbf{9}} boldsymbol{a} boldsymbol{r}(operatorname{trap} . boldsymbol{X} boldsymbol{Y} boldsymbol{B} boldsymbol{A}) )
8
96If ( A(-2,-1), B(a, 0), C(4, b) ) and ( D(1,2) ) are
the vertices of a parallelogram, find the
values of a and b.
8
978. In figure, RENT is a rectangle. Its diagonals meet at O. Find
x. ifOR=2x + 4 and OT=3x + 1.
3x + 1
2x+4
8
98Which of the following is different from
the other three?
( mathbf{A} )
( B )
( mathbf{C} )
D.
8
99ITSUMUTULUI0IU OUT
6.
7
In a parallelohram opposite angles are not equal.
Ferrhombuis kite
8
100The radius of a circles ( 17 mathrm{cm} ) and the
length of one of its chord is ( 16 mathrm{cm} ). Find
the distance of the chord from the
centre
8
101Find ( (x, y) ) if ( (3,2),(6,3),(x, y) ) and (6,5) are the vertices of a parallelogram
A . (9,6)
B. (6,6)
( c .(9,9) )
D. None of these
8
102ES
120°
11.
70°
IC
In the above figure both RISK and CLUE are parallelograms.
Find the value of x.
Cindthemen.nf and Zsif SPRO in Fig (If you
8
103Assertion : The adjacent angles in a parallelogram are
supplementary,
Reason: In a parallelogram, the adjacent angles are always
equal.
8
104The exterior angle of a regular polygon
is ( 24^{circ} )
Find the number of sides of this regular polygon.
8
105In a regular pentagon ( A B C D E ; A C )
and ( B E ) intersect at ( P . ) Calculate the
angles ( C B E ) and ( B P A )
( A cdot 30^{circ} ) and ( 60^{circ} )
B. ( 72^{circ} ) and ( 108^{circ} )
c. ( 54^{circ} ) and ( 108^{circ} )
D. ( 72^{circ} ) and ( 72^{circ} )
8
106Let ( F_{1} ) be the set all of parallelograms, ( F_{2} )
be the set of the rectangles, ( F_{3} ) be the
set of rhombuses, ( F_{4} ) be the set of
squares ( F_{5} ) be the set of trapezium in a
plane then ( F_{1}= )
A. ( F_{2} cap F_{3} )
B. ( F_{2} cup F_{3} cup F_{4} )
c. ( F_{3} cup F_{4} cup F_{5} )
D. ( F_{3} cap F_{1} )
8
107If the sides ( A B, B C, C D ) and ( D A ) of a trapezium ABCD measure ( 10 mathrm{cm}, 20 mathrm{cm} )
( 18 mathrm{cm} ) and ( 16 mathrm{cm} ) respectively then find the length of the longer diagonal given
that ( A B ) is parallel to ( C D )
A ( . sqrt{760} mathrm{cm} )
В. ( sqrt{231} mathrm{cm} )
( c cdot sqrt{54} c m )
D. ( sqrt{930} mathrm{cm} )
8
108If non parallel sides of a trapezium are equal, prove that it is cyclic.8
109Polygons are figures.
A. many sided
B. one sided
c. has no sides
D. two sides
8
110In the figure at right, ( A B C D ) is a
parallelogram ( angle B A O= )
( mathbf{3 0}^{circ}, angle boldsymbol{D A O}=angle mathbf{4 5}^{circ} ) and ( angle boldsymbol{C O D}= )
( mathbf{1 0 5}^{circ} . ) Calculate
( angle C B D )
A ( cdot 60^{circ} )
B. 30
( c cdot 20 )
D. None of these
8
111The interior angles of a polygon are in arithmetic progression. The smallest angle is ( 120^{circ} ) and the common
difference is ( 5 . ) Find the number of sides
of the polygon.
8
1127. In trapezium HARE, EP and RP are bisectors of Z E and
Rrespectively. Find Z HAR and ZEHA.
ER250 30°
P
15.
8
113In ancient India, the shapes of altars used for house hold rituals were
A. squares and circles
B. triangles and rectangles
c. trapeziums and pyramids
D. rectangles and squares
8
1144.
All squares and rectangles are also parallelograms.
Tf1
1:
1 ito luas as
8
115Calculate the sum of angles of a
polygon having 10 sides.
A ( .960^{circ} )
B. ( 1440^{circ} )
c. ( 900^{circ} )
D. 720
8
116B
6. In a parallelogram ABCD, the bisectors of Z A and
meet at O. Find ZAOB.
8
117Explain how square is a quadrilateral.
A. All angles are equal
B. Because it is four sided
c. Two sides are equal
D. None of these
8
118n quadrilateral ABCD ( angle mathrm{B}=90^{circ}, angle mathrm{C}-angle )
( mathrm{D}=mathbf{6 0}^{circ} ) and ( angle mathbf{A}-angle mathbf{C}-angle mathbf{D}=mathbf{1 0}^{circ} . ) Find
( A, angle C ) and ( angle D )
8
119The diagonals ( A C ) and ( B D ) of a
parallelogram ( A B C D ) intersect each
other at the point ( O )
If ( angle D A C=32^{circ} ) and ( angle A O B=70^{circ}, ) then
( angle D B C ) is equal to?
A ( cdot 24^{circ} )
B. ( 86^{circ} )
( c cdot 38^{circ} )
( D cdot 32^{circ} )
8
120One of the diagonals of a rhombus is equal to a side of the rhombus. The
angles of the rhombus are
( mathbf{A} cdot 60^{circ} a n d 80^{circ} )
B ( cdot 60^{circ} ) and ( 120^{circ} )
c. ( 120^{circ} ) and ( 240^{circ} )
D. ( 100^{circ} ) and ( 120^{circ} )
8
1215.
In a quadrilateral ABCD, ZB = 90° and
AD2 = AB2 + BC2 + CD2 then ZACD is equal to
(a) 90°
(b) 60°
(c) 30°
(d) None of these
8
122.has the same properties of that of a rhombus but not a rectangle.
A. Square
B. Parallelogram
c. Trapezium
D. Kite
8
123The difference between an interior angle
of ( (n-1) ) sided regular polygon and an
interior angle of ( (n+1) ) sided regular
polygon is ( 9^{circ} . ) Find the value of ( n )
( A cdot 3 )
B. 4
( c .9 )
D. 12
8
124In the following figure, ABCD to a
trapezium with ( A B | D C ). If ( A B=9 mathrm{cm}, D C= )
( 18 mathrm{cm}, mathrm{CF}=13.5 mathrm{cm}, mathrm{AP}=6 mathrm{cm} ) and
BE=15 cm. Calculate PE
( A cdot P E=5.8 mathrm{cm} )
3. ( P E=4.8 mathrm{cm} )
( c cdot P E=2.8 mathrm{cm} )
( P E=3.8 mathrm{cm} )
8
125Find the area of ( square A B C D )
( mathbf{A} cdot 4(24+25 sqrt{3}) c m^{2} )
B ( cdot 4(25+24 sqrt{3}) c m^{2} )
( mathbf{c} cdot 2(24+25 sqrt{3}) c m^{2} )
D. None of these
8
126Find ( x )8
127( A B C D ) and ( P Q R C ) are rectangle where
( Q ) is the mid-point of ( A C . ) Prove that
( boldsymbol{D} boldsymbol{P}=boldsymbol{P C} )
8
128( A B C ) is a right-angled triangle and 0 is
the mid point of the side opposite to the right angle. Explain why 0 is equidistant from ( A, B ) and ( C ) (The dotted lines are drawn additionally to help you)
8
129In a trapezium ( mathrm{ABCD}, mathrm{AB}|| mathrm{CD} . ) If ( angle boldsymbol{A}= )
( 60^{circ} ) then ( angle D=? )
A ( .100^{circ} )
B. ( 120^{circ} )
( c cdot 70 )
D. 300
8
130State true or false:
The bisector of any two adjacent angles of a rhombus form a right-angled triangle.
A. True
B. False
8
131( A B C D ) is a rhombus with ( angle A B C= )
( 56^{circ}, ) then ( angle A C B ) will be
A ( .56^{circ} )
B. ( 124^{circ} )
( c cdot 62^{0} )
D. ( 34^{circ} )
8
132n the figure, two identical regular
hexagons are placed side by side as shown, then find the value of z.
A ( cdot 60^{circ} )
В. ( 90^{circ} )
( c cdot 120^{circ} )
D. ( 160^{circ} )
8
133Three angles of a seven sided polygon
are ( 132^{circ} ) each and the remaining four
angles are equal. Find the value of each equal angle.
A .125
B. ( 156^{circ} )
( c cdot 126^{circ} )
D. ( 130^{circ} )
8
134In a polygon, there are 5 right angles and the remaining angles are equal to
( mathbf{1 9 5}^{circ} ) each. Find the number of sides in
the polygon.
A . 5
B. 11
c. 8
D. 7
8
135Points ( X ) and ( Y ) are taken on the sides
QR and RS, respectively of a parallelogram PQRS, so that ( Q X=4 X R ) sand ( mathrm{RY}=4 mathrm{YS} ). The line ( mathrm{XY} ) cuts the line
PR at Z. Find the ratio PZ:ZR.
( mathbf{A} cdot 4: 21 )
в. 3: 4
c. 21: 4
D. 4: 3
8
136Diagonals ( boldsymbol{A C} ) and ( boldsymbol{B D} ) of a
trapezium ( boldsymbol{A B C D} ) with ( boldsymbol{A B} | boldsymbol{D C} )
intersect each other at ( O . ) Prove that
( boldsymbol{a} boldsymbol{r}(boldsymbol{A O D})=boldsymbol{a r}(boldsymbol{B O C}) )
8
137How many diagonals does each of the following have?
(b) A regular hexagon
(c) A triangle
8
138In a polygon, there are 5 right angles and the remaining angles are equal to
( 195^{circ} ) each., Find the number of sides in
the polygon.
8
13919
NL, Wily
Construct a trapezium ABCD where AB | CD, AD =
BC=3.2 cm, AB=6.4 cm and CD=9.6 cm. Measure B
and ZA.
6.4 cm
A
3.2 cm
3.2 cm
13.2 cm
1600
D4
9.6 cm
[Hint : Difference oftwo parallel sides given an equilateral
triangle.]
8
140In the circle with centre ( boldsymbol{O}, boldsymbol{P Q} ) and ( boldsymbol{R S} )
are diameters. ( M ) and ( N ) are points on
the arcs ( Q R ) and ( Q S ) respectively and
( boldsymbol{R} boldsymbol{X}=boldsymbol{S} boldsymbol{Y} ) then ( boldsymbol{P} boldsymbol{X} boldsymbol{Q} boldsymbol{Y} ) is a
parallelogram.
A. True
B. False
8
14158. If ABCD is a parallelogram in
which ZA = 60°, AB = 5 cm, BC
= 4 cm and the bisectors of ZA
and LB meet at point P lying on
side CD, then what will be the
value of PD?
(1) 4 cm (2) 5 cm
(3) 3 cm (4) 6 cm
8
142Find the fourth vertex of the
parallelogram whose consecutive
vertices are (8,4),(5,7),(-1,1)
8
143( P Q, Q R ) and ( R S ) are three consecutive
sides of a regular polygon. If ( <Q P R= )
( 20^{circ} ) find the number of side in the
polygon.
8
14410. Find measure.x.
9001
500
110°
1 Lat PORS hea rhombus find
y
8
145( A B=D C=8 c m, A D=4 c m ) what
should be the length of side ( B C ), if
( A B C D ) is parallelogram
A. ( 4 c m )
B. 8 cm
( mathbf{c} cdot 16 c m )
D. None of the above
8
146Number of diagonals in parallelogram is/are:
A. 0
B.
( c cdot 2 )
D. none of these
8
147The diagonals of a parallelogram
( A B C D ) intersect at ( O . A ) line through
intersect ( A B ) at ( X ) and ( D C ) at ( Y ). Identify
the correct option
A. ( O X=O Y )
в. ( O X>O Y )
c. ( O X<O Y )
( cdot O X-O Y=0 )
0
8
148The figure obtained by joining the midpoints of the sides of a rhombus taken
in order is
A . a square
B. a rhombus
c. a rectangle
D. parallelogram
8
149( A B C D ) is a rectangle in which diagonal
( B D ) bisects ( angle B . ) Show that ( A B C D ) is a
square.
8
150In the given figure, ( P Q R S ) is a square
and ( angle B A C=90^{circ} . ) Prove that ( : R S^{2}= )
BRxSC
8
151Find area of trapezium whose parallel
sides ( 9 mathrm{cm} ) and ( 5 mathrm{cm} ) respectively and
the distance between these sides is
( mathbf{8} c boldsymbol{m} )
8
15215. Explain how the following figure is a trapezium? Which of
its two sides are parallel ?
100.90
802
8
15355. The radius and the height of a
cone are in the ratio 4: 3. The
ratio of the curved surface area
and total surface area of the cone
(1) 5:9
(3) 5:4
(2) 3:7
(4) 16:9
8
1542.
In the given figure, ABCD is a quadrilateral and
ZADC = “. ZBCD=bº. AO and BO are bisectors of
ZDAB and ZABC respectively meeting at O. Find ZAOB
in terms of aand b.
DO
8
155Find the number of sides of a regular
polygon if each interior angle is ( 135^{circ} )
8
156The radius of the locus by the point represented by ( z, ) when ( arg frac{z-1}{z+1}=frac{pi}{4} )
is
A ( cdot sqrt{2} )
B. ( sqrt{2} pi )
c. ( frac{pi}{sqrt{2}} )
D. none of these
8
157Say True or False. All the sides of a parallelogram are of equal length.
A. True
B. False
8
158( A B C D ) is a trapezium in which ( A B | ) ( D C, A B=16 mathrm{cm} ) and ( D C=24 mathrm{cm} . ) If
( E ) and ( F ) are respectively the midpoints of ( A D ) and ( B C, ) then ( a r(A B F E)= ) ( frac{9}{11} a r(E F C D) )
A . True
B. False
8
159One angle of a seven sided polygon is
( 108^{circ} ) and each of the other six angles is
( x^{circ} . ) The value of ( x ) is
( mathbf{A} cdot 114^{circ} )
B. ( 121^{circ} )
( mathrm{c} cdot 131^{circ} )
D. ( 132^{circ} )
8
160The ratio of the area of a square to that
of the square drawn on its diagonal is?
A . 1:
B. 2:
c. 1: 2
D. 1: 4
8
161Find the area of a rhombus, each side of
which measures ( 20 mathrm{cm} ) and one of
whose diagonals is ( 24 mathrm{cm} )
8
162( A B C ) is a right angled triangle and 0 is
the mid point of the side opposite to the
right angle. Explain why ( O ) is
equidistant from ( A, B ) and, ( C )
8
1633.
In the following figure RISK and CLUE are parallelograms.
Then the measure of x is 10kº. Find the value of k.
К
.
E SU
120°
700
I
C
8
164Find the area of a rhombus if its
vertices are (3,0),(4,5),(-1,4) and (-2,-1) taken in order
8
165A parallelogram is cut by two set of ( boldsymbol{m} )
lines parallel to its sides. The number of
parallelogram thus force is
A ( cdotleft(^{m} C_{2}right)^{2} )
B. ( left(^{m+1} C_{2}right)^{2} )
( mathbf{c} cdotleft(^{m+2} C_{2}right)^{2} )
D. ( m+1 C_{2} )
8
166A ( ldots . . . . . . . . . . . . ) has 4 sides equal and 4 right
angles.
A . square
B. parallelogram
c. trapezium
D. rectangle
8
167Position of P is
A. Interior of curve
B. Exterior of curve
c. on the curve
D. can not be said
8
168PQRS is a square E and F are points on the sides ( Q R ) and ( R S ) respectively show
that ( boldsymbol{a r}(boldsymbol{Delta} boldsymbol{P Q} boldsymbol{E})=boldsymbol{a r}(boldsymbol{Delta} boldsymbol{P S F}) )
8
169How many sides does a Decagon have?
A. 7
B. 8
( c cdot 9 )
D. 10
8
170If the straight line ( x cos alpha+y sin alpha= )
( p ) touches the curve ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1, ) then
prove that ( boldsymbol{a}^{2} cos ^{2} boldsymbol{alpha}+boldsymbol{b}^{2} sin ^{2} boldsymbol{alpha}=boldsymbol{p}^{2} )
8
1711.
All squares are also rectangles.
8
1722.
(a) 60°
(b) 120
(c) 180°
(d) none of these
8
173Points ( P ) and ( Q ) have been taken on
opposite sides ( A B ) and ( C D )
respectively of a parallelogram ( A B C D ) such that ( A P=C Q . ) Show that ( A C ) and
( P Q ) disect each other.
8
17456. A parallelogram ABCD has sides
AB = 24 cm and AD = 16 cm.
The distance between the
sides AB and DC is 10 cm. Find
the distance between the sides
(1) 16 cm (2) 18 cm.
(3) 15 cm. (4) 26 cm.
8
175The number of triangles are less than the number of sides formed
by the diagonals from one vertex.
( A cdot 3 )
B. 5
( c cdot 8 )
D.
8
176Which of the following properties are not true for a
parallelogram?
(a) Its diagonals are equal.
(b) Its diagonals are perpendicular to each other.
© The diagonals divide the figure into four congruent
triangles.
(d) Each diagonal divides a parallelogram into two
congruent triangles.
8
17717. The adjacent figure PQRS is a trapezium in which SP ||RQ,
find the measures of ZP and ZR.
So
6.
8
178In given figure ( A B C D ) is a rhombus. If
( angle B A C=38^{circ}, ) find:
( angle A D C )
8
179State true or false:
( A B C D ) is a parallelogram. ( P ) and ( Q ) are the mid-points of sides ( A B ) and ( A D ) respectively. Hence, area of triangle ( A P Q=frac{1}{8} ) of
the area of parallelogram ( A B C D )
A. True
B. False
8
180Which statement is true about the
figure formed by joining the midpoints
of the adjacent sides of a rectangle with
( operatorname{sides} 8 c m ) and ( 6 c m ? )
A . It is a rectangle of area ( 24 mathrm{cm}^{2} )
B. It is a square of area ( 24 mathrm{cm}^{2} )
C. It is a trapezium of area ( 24 mathrm{cm}^{2} )
P. It is a rhombus of area ( 24 mathrm{cm}^{2} )
8
181If the sum of adjacent angles of a
quadrilateral is equal to ( 180^{circ}, ) then
A . a parallelogram
B. connex
c. concave
D. none of the above
8
182The ratio of two adjacent sides of a parallelogram is 2: 3 and its perimeter
is ( 50 mathrm{cm} . ) Find its area if altitude
corresponding to large side is ( 10 mathrm{cm} )
8
183angles.
The diagonals of a square bisect each other at right angles.
9.
8
184The ratio of two sides of parallelogram
is 3: 5 and its perimeter is ( 48 mathrm{cm} . ) Find the sides of the parallelogram
8
185Let ( A B C D ) is a square with sides of
unit length.Points E and F are taken on
( operatorname{sides} A B ) and ( A D ) respectively so that
( A E=A F ).Let ( P ) be a point inside the
( square A B C D )
Let a line passing through point ( boldsymbol{A} ) divides the square ( square A B C D ) into two
parts so that area of one portion is double the other, then the length of portion of line inside the square is
A. ( frac{sqrt{10}}{3} )
B. ( frac{sqrt{13}}{3} )
c. ( frac{sqrt{11}}{3} )
D. ( frac{2}{sqrt{3}} )
8
186If ABCD is a parallelogram in which and ( Q ) are the centroids of ( Delta A B D ) and
( Delta B C D, ) then, PQ equals:
( A cdot A Q )
B. AP
c. ВР
D. DQ
8
187Sum of measures of angles of a
Nonagon is ( 1260^{circ} . ) Find how much each
angle is measured.
A ( cdot 100^{circ} )
B . ( 140^{circ} )
( c cdot 108^{circ} )
D. ( 90^{circ} )
8
188Sum of the interior angles of a regular
polygon is ( 1620^{circ} . ) How many sides does
this polygon have?
8
189( A B, B C ) and ( C D ) are the three consecutive
sides of a regular polygon. If ( angle B A C= )
( 15^{circ} . ) Find each interior angle of the
polygon.
A ( .147^{circ} )
B. 162
( c cdot 150 )
D. ( 140^{circ} )
8
190If the sum of measures of two angles of
a hexagon is ( 220^{circ}, ) then what is the sum of the measures of other four angles?
A . ( 800^{circ} )
B. ( 700^{circ} )
( c cdot 600^{circ} )
D. ( 500^{circ} )
8
191A quadrilateral whose all sides are equal and has four right angles is called
( a )
A. rectangle
B. rhombus
c. kite
D. square
8
1928.
then x not equal to
D550

65°
HBrown
A
60°y Porno
(a) 55º.
(c) 650
(b) 60° s
(d) 50°
ed
8
193( A B C D ) is a trapezium in which ( A B|| D C ) and its diagonals intersect
each other at point ( ^{prime} boldsymbol{O}^{prime} ). Show that ( frac{A O}{B O}=frac{C O}{D O} )
8
194Show that if the diagonal of a quadrilateral bisect each other at right angles,then it is a rhombus8
195If all the angles of a 14 -sided figure are equal, then the measure of each angle is equal to?
( ^{A} cdotleft(184 frac{2}{7}right)^{circ} )
B. ( left(164 frac{2}{7}right) )
( ^{c} cdotleft(134 frac{2}{7}right)^{circ} )
( ^{mathrm{D}} cdotleft(154 frac{2}{7}right) )
8
1961.
Find the sum of interior angles of
(1) a polygon with 12 sides.
(ii) a polygon with 18 sides.
Doch interior angle of remular noloon is 1440 Find
8
197A square is a
A. kite
B. trapezium
C . triangle
D. rhombus
8
198ITU MUTUICdSUIC UTCdnUI C U15″
9.
The following figures GUNS and RUNS are rarallelograms.
Find x and y: (Length are in cm)
26
واG
3y – 1
+ x
y
91
+
7
8
199The perimeter of a parallelogram is 150
( mathrm{cm} ) and one of its side is greater than
the other by ( 25 mathrm{cm} . ) Find the lengths of all the sides of that parallelogram
8
200In the following figure, ( A B C D ) is a rhombus and ( D C E F ) is a square.
If ( angle A B C=56^{circ} ), find
( angle D A E )
( angle boldsymbol{F} boldsymbol{E} boldsymbol{A} )
( angle E A C )
( angle A E C )
+ Option
8
201If the diagonals of a quadrilateral are perpendicular to each other, the figure would always be included under the general classification:
A. rhombus
B. rectangle
c. square
D. isosceles trapezoid
E. none of these
8
202The difference between an exterior
angle of ( (n-1) ) sided regular polygon and an exterior angle of ( (n+2) ) sided regular
polygon is ( 6^{circ} . ) Find the value of ( n )
( A cdot 13 )
B. 12
( c cdot 16 )
D. 18
8
203( A B C D ) is a rectangle ( A C ) is diagonal
Find the angles of ( triangle A C D . ) Give reasons
8
2041.
To construct a parallelogram, the minimum number of
measurements required is:
(a) 2
(b) 3
(d) 1
(c) 4
8
205In the fig, ( square P Q R S ) and ( square A B C R ) are
two parallelograms.
f ( angle P=110^{circ} ) then find the measures of
all angles of ( square A B C R )
8
206In the figure, ( A B C D ) is a rectangle,
( triangle C E F ) is an equilateral triangle. Find ( x )
A ( cdot 25^{circ} )
B. ( 30^{circ} )
( c cdot 20^{circ} )
0.50
8
2072.
Assertion : In all cases of quadrilateral, it is convenient
and helpful to draw rough sktech of the
quadrilateral and indicate the data on it.
Reason : This suggest the steps of construction.
8
208Each interior angle of a ( n ) -sided
regular polygon is ( 162^{circ} . ) Find the interior
angle of another polygon with ( 2 n ) sides.
A . ( 155^{circ} )
B . ( 160^{circ} )
( c cdot 171 )
D. one of the above
8
209Fill in the blanks using the correct word given in brackets:
Two polygons of the same number of sides are similar, if (a) their corresponding angles are and
(b) their
corresponding sides are ( ldots ) proportional).
8
210Which of the following is not the
property of a square?
A. Each angle of a square is a right angle
B. The diagonals of a square are not equal
C. The sides of a square are equal
D. The diagonals of a square bisect each other right angle
8
2114.
A rhombus has all its sides of
8
212Find the area of the figure bounded by the following curves
( y=sin x_{2}, y=2 x / pi )
8
2131. In Fig. PQRS is a square. Determine ZSRP.8
214Ina parallelogram ( A B C D ) the bisector
of ( angle A ) also bisects ( B C ) at ( X . ) prove that
( A D=2 A B )
8
215( A B C D ) is a parallelogram, ( A E ) is
perpendicular to ( D C, ) If ( D C=20 mathrm{cm} )
( A D=5 mathrm{cm} ) and the area of the
parallelogram is ( 40 mathrm{cm}^{2} ). Find ( D E )
8
216The sides BA and DC of quadrilateral ABCD are produced
as shown in the figure given below. Then x + y is equal to
CF

E
A
(a) a+b (b) a-b
(0)
(d)
8
217One side of a parallelogram is ( frac{3}{4} ) times its adjacent side. If the perimeter of the parallelogram is ( 70 mathrm{cm}, ) find the sides of the parallelogram.8
218B
15. Consider the following parallelograms. Find the values of
the unknown x, y, z.
Dy
0001
30
(iv)
800
1129
8
219In the given isosceles trapezium ABCD,
( boldsymbol{A B} | boldsymbol{D C} ) and ( boldsymbol{A D}=boldsymbol{B C} ). If ( angle boldsymbol{D}= )
( 60^{circ}, A B=18 c m ) and ( A D=12 c m, ) find
the length of DC
A . ( 60^{circ} )
B. ( 30^{circ} )
( c cdot 90 )
D. ( 20^{circ} )
8
22014. In the following figure, AB || DC and AD = BC. Find the
value of x.
20 cm
10 cm
60°
JB
-x cm-
8
221In the given figure, ( A B C D ) is a
rhombus in which ( angle B C D=110^{circ}, ) find
( (x+y) )
8
222Diagonals ( A C ) and ( B D ) of a parallelogram ABCD intersect each other at ( 0 . ) If
( O A=3 mathrm{cm} ) and ( O D=2 mathrm{cm} ) determine
the lengths of ( A C ) and ( B D )
8
223The four angles of a quadrilateral are equal. Draw this quadrilateral in your notebook. Find each of them.
A. ( 60^{circ}, 120^{circ}, 30^{circ}, 150^{circ} )
( ^{circ} )
B. ( 60^{circ}, 120^{circ}, 60^{circ}, 120^{circ} )
( mathbf{c} cdot 90^{circ}, 90^{circ}, 90^{circ}, 90^{circ} )
D. ( 60^{circ}, 60^{circ}, 120^{circ}, 120^{circ} )
8
224In the given figure, ( A B | ) DC Prove that(i) ( triangle D M U sim triangle B M V(text { ii) } D M times B V= )
( boldsymbol{B} boldsymbol{M} times boldsymbol{D} boldsymbol{U} )
8
225Vertices of a parallelogram ( A B C D ) are
( boldsymbol{A}(mathbf{3}, mathbf{1}), boldsymbol{B}(mathbf{1 3}, mathbf{6}), boldsymbol{C}(mathbf{1 3}, mathbf{2 1}) ) and
( D(3,16) . ) If a line passing through the origin divides the parallelogram into two congruent parts then the slope of the line is
A ( cdot frac{11}{12} )
в. ( frac{11}{8} )
c. ( frac{25}{8} )
D. ( frac{13}{8} )
8
226State whether the following statements
are true of false
Circles with same radii are equal
A. True
B. False
8
227The measures of two complements are
( x ) and ( (x+50)^{circ} . ) Find the measure of
each of them
8
228Polygons that have any portions of their diagonals in their exterior are called
A. squares
B. convex polygons
c. concave polygons
D. triangles
8
229Find the number of sides of a regular polygon if each exterior angle is equal
to one third of its adjacent interior
angle
8
230Prove that a diagonals of a parallelogram divides it into two congruent triangles.8
231The sides of a hexagon are produced in order. If the measures of exterior angles
so obtained are ( (6 x-1)^{circ},(10 x+ )
2) ( ^{circ},(8 x+2)^{circ},(9 x-3)^{circ},(5 x+4)^{circ} ) and
( (12 x+6)^{circ} ; ) Find each exterior angle
B . ( 41^{circ}, 86^{circ}, 56^{circ}, 60^{circ}, 39^{circ}, 80^{circ} )
C ( cdot 41^{circ}, 72^{circ}, 58^{circ}, 60^{circ}, 39^{circ}, 90^{circ} )
D. ( 41^{circ}, 82^{circ}, 60^{circ}, 60^{circ}, 36^{circ}, 100 )
8
232In the following figure, ABCD is a parallelogram and EFCD is a rectangle. Also, ( A L perp D C . ) Prove that
(i) ( operatorname{ar}(mathrm{ABCD})=operatorname{ar}(mathrm{EFCD}) )
(ii) ( operatorname{ar}(mathrm{ABCD})=mathrm{DC} times mathrm{AL} )
8
2335.
6.
yuu alu Teulallgles are also paralluogo.
If the diagonals of a rhombus are equal, its always a square.
In a parallelohram opposite angles are not equal
8
234In square PQRS. if ( mathrm{PQ}=3 x-7 ) and
( Q R=x+3 ; ) find PS
( A cdot 6 )
B. 7
( c cdot 8 )
D. 5
8
235In the figure(not drawn to scale), ABCD
is a rhombus, ABE is a straight line.
Find ( angle mathrm{DBE} )
A . 150
B. ( 152^{circ} )
( mathbf{c} cdot 153^{circ} )
D. ( 156^{circ} )
8
2368.
Find the number of sides of a polygon whose exterior and
interior angles are in the ratio 1:5.
8
237ff ( A(-2,1), B(a, 0), C(4, b) ) and ( D(1,2) )
are the vertices of parallelogram ( A B C D, ) find ( a ) and ( b . ) Hence find the length of it’s sides.
8
238IV
3. In Fig, bisectors of B and 2D of quadrilateral ABCD
meet CD and AB produced at P and respectively. Prove
that P+2Q=
BQ
W
PD
8
239ABCD is a trapeziumin which AB is parallel to DC. If the diagonals intersect at ( 0, ) then which one of the following is
correct?
A ( cdot frac{O A}{O C}=frac{O B}{O D} )
в. ( frac{A D}{B C}=frac{A B}{D C} )
c. ( frac{O B}{O D}=frac{B C}{C D} )
D. ( frac{O A}{O C}=frac{D A}{D C} )
8
240ABCD is a parallelogram, ( A E perp D C ) and ( boldsymbol{C F} perp boldsymbol{A D} . ) If ( boldsymbol{A B}=mathbf{1 6} mathrm{cm}, boldsymbol{A} boldsymbol{E}=mathbf{8} c boldsymbol{m} )
and ( boldsymbol{C F}=mathbf{1 0} mathrm{cm}, ) find ( boldsymbol{A} boldsymbol{D} )
8
241How many sides does a regular polygon have if the measure of an exterior angle
is ( 24^{0} ? )
A . 14
B. 13
c. 15
D. 18
8
242Is it possible to have a polygon, whose sum of interior angles is ( 870^{circ} )
State true or false:
A. True
B. False
8
243The three vertices of a parallelogram taken in order are (-1,0),(3,1) and (2,2) respectively.Find the coordinates of the fourth vertex8
244The measure of the external angle of a
regular octagon is
( mathbf{A} cdot pi / 4 )
в. ( pi / 6 )
c. ( pi / 8 )
D. ( pi / 12 )
8
245If one angle of a parallelogram is ( 65^{circ} )
What are the other angles?
A ( .50^{circ}, 120^{circ}, 50^{circ} )
в. ( 115^{circ}, 65^{circ} ), ( 115^{circ} )
( mathbf{c} cdot 65^{circ}, 115^{circ}, 65^{circ} )
D. None of the above
8
2468. In the following figure of a ship, ABDH and CEFG are two
parallelograms. Find the value of x.
300
130°
C
D
8
247The angles of a pentagon are in the ratio ( 4: 8: 6: 4: 5 . ) Find each angle of
the pentagon.
A ( cdot 40^{circ}, 160^{circ}, 120^{circ}, 80^{circ} )and ( 100^{circ} )
B . ( 60^{circ}, 160^{circ}, 120^{circ}, 80^{circ} ) and ( 100^{circ} )
c. ( 80^{circ}, 160^{circ}, 120^{circ}, 80^{circ} ) and ( 100^{circ} )
D. ( 30^{circ}, 160^{circ}, 120^{circ}, 80^{circ} ) and ( 100^{circ} )
8
ZA and B respectively. Prove that 2 403 =
1 / 1 / C + LD)
8
249( A B C D ) is a trapezium with parallel
( operatorname{sides} A B=a c m ) and ( D C=b c m . E )
and ( F ) are the mid-points of the non-
parallel sides. The ratio of ( a r(A B F E) )
and ( a r(E F C D) ) is
( A cdot a: b )
B. ( (3 a+b):(a+3 b )
( c cdotleft(a+3 b_{cdot}(3 a+b)right. )
D. ( (2 a+b):(3 a+b) )
8
250ABCD is parallelogram and ABEF is a rectangle and DG is perpendicular on
AB
Prove that (i) ( a r(A B C D)= )
( a r(A B E F) )
(ii) ( a r(A B C D)=A B times D G )
8
251State true false:
It is possible to have a polygon whose
sum of interior angles is ( 630^{circ} )
A. True
B. False
8
252Is it a closed curve?8
253In a parallelogram ABCD if ( A B=2 x+5 ) ( mathrm{CD}=mathrm{y}+1, mathrm{AD}=mathrm{y}+5 ) and ( mathrm{BC}=3 mathrm{x}-4 ) then ratio
of ( A B: B C ) is
( A cdot 71: 21 )
B. 12:11
c. 31: 35
D. 4 : 7
8
254PQRS is a parallelogram. If ( L, M ) are
the midpoints of ( Q R ) and ( P S )
respectively, and ( O ) is any point on ( L M )
then the area of triangle ( O P Q ) is equal
to
A ( cdotleft(frac{1}{3}right)^{r d} ) of the parallelogram ( P Q R S )
B ( cdotleft(frac{1}{4}right)^{t h} ) of the parallelogram ( P Q R S )
C ( cdotleft(frac{1}{2}right) ) of the parallelogram ( P Q R S )
D ( left(frac{1}{6}right)^{t h} ) of the parallelogram ( P Q R S )
8
2559.
In the isosceles trapezium PQRS with PQ || RS and
QR = PS, which of the following is correct?
(a) ZP+ZS=180° and ZQ+ZR=180°
(b) PS = QR and PR = QS
(c) ZP=2Q and ZR= ZS
(d) All of the above
8
2561.
To construct a quadrilateral, if 3 angles are given then
how many included sides are required.
8
257Find the measure of each exterior angle
of a regular polygon of 15 sides
A ( cdot 24^{circ} )
B. ( 30^{circ} )
( c cdot 36^{0} )
D. ( 42^{circ} )
8
2585.
Given AB = 3 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm,
CD = 2 cm. Which of the following is false about the
(a) It is possible to draw the quadrilateral.
DC<AC.
<AC
(d) None of these
8
259The slope of a curve at each of its points is equal to the square of the abscissae of the point. Find the particular curve through the point (-1,1)8
260Prove that parallelograms are on the
same base and between the same
parallel lines are equal in area.
8
261An exterior angle of regular polygon is ( 12^{circ} ) the sum of all the interior angles is
A ( cdot 4040^{circ} )
B . ( 5040^{circ} )
c. ( 6040^{circ} )
D. ( 7040^{circ} )
8
2622.
To construct a quadrilateral, if 2 diagonals are given, then
how many sides are required.
8
263A polygon has 44 diagonals. Find the number of its sides.8
2642.
All rectangles are also squares.
8
265Let ABCD be a parallelogram. Let AP, CQ be the ( perp ) from ( A ) and ( C ) on its diagonal
BD. Which of the following is true. This question has multiple correct options
A. ( C Q=P D )
в. ( P D=Q B )
c ( . A P=C Q )
D. ( A P=B Q )
8
266The interior angle of a regular polygon is
( mathbf{1 5 6}^{circ} ). Find the number of sides of the
polygon.
8
267In the figure, find the measure of
( angle M P N )
8
268The area of the parallelogram ABCD is
( 90 c m^{2}(text { see Fig.9.13 ) EC }=F D . ) Find
( boldsymbol{A}(boldsymbol{A} boldsymbol{B} boldsymbol{E} boldsymbol{F}) )
( mathbf{A} cdot 45 c m^{2} )
B. ( 60 mathrm{cm}^{2} )
( mathrm{c} cdot 90 mathrm{cm}^{2} )
D. ( 180 mathrm{cm}^{2} )
8
2695.
In the given parallelogram YOUR, Z RUO= 120° and OYis
extended to point S such that Z SRY= 50°. Find YSR
U
12000
8
270Find the area ( left(text { in } m^{2}right) ) of the trapezium
PQRS with height PQ given in the figure.
8
271Measures of opposite angles of
parallelogram are ( (3 x-2)^{circ} ) and ( (50- )
( x)^{circ} . ) Find the measure of its other
angles.
A . 143
в. 153
( c cdot 163 )
D. 173
8
2729.
If two adjacent angles of a parallelogram are in the ratio
4:5, then the measure of the angles not equal to is
(a) 80°, 100°
(b) 160°, 200°
(c) 40°,50°
(d) 114°, 36°
8
27353. The difference between the exte-
rior and interior angles at a ver-
tex of a regular polygon is 150°.
The number of sides of the poly-
gon is
(1) 10
(2) 15
(3) 24
(4) 30
8
274The triangle, quadrilateral, pentagon are all examples of
A. diagonal
B. open curve
c. polygon
D. circles
8
275In a regular polygon, the exterior and interior angles are in the ration 1: 4
The number of sides of the polygon is
A . 10
B. 12
c. 15
D. 16
8
276If ( A B C D ) is a parallelogram and ( Q ) and ( R )
are the circumcentres of the triangles ( A B C ) and ( A D C ) respectively, then ( A Q C R ) is always
A. A rectangle
B. A trapezium
c. A rhombus
D. None of these
8
277measurements can determine a
8
2787.
IfABCD is a parallelogram, then ZA-ZC=………..
. 100
8
279How many diagonals does a triangle have?
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
( D )
8
280The number of sides of two regular polygons A and B are in ratio 1: 3. If each
interior angle of polygon ( mathrm{B} ) is ( 168^{circ} . ) Find each interior angle of polygon ( A )
A ( .144^{circ} )
B. 120
( c cdot 72 )
D. 22.5
8
281In a square ( A B C D, angle A B D=3 x= )
( angle A D B, ) then ( angle B D C ? )
( mathbf{A} cdot 6 x^{circ} )
B. ( (90-6 x)^{text {d }} )
( mathbf{c} cdot 45^{circ} )
D. None
8
282( A B C D ) is a rhombus and ( P, Q, R ) and ( S )
are the mid-points of the sides ( A B, B C, C D ) and ( D A ) respectively.
Show that the quadrilateral ( P Q R S ) is a
rectangle
8
283Find the measure of ( angle P, ) if ( overline{S P} | overline{R Q} ) in
the given figure.
8
284In fig. ABCD is a parallelogram. What
are the values of ( p ) and ( q ? )
If ( angle C B E=100^{circ} )
( mathbf{A} cdot angle p=100^{circ}, angle q=80^{circ} )
B . ( angle p=80^{circ}, angle q=100^{circ} )
c. ( angle p=angle q )
D. None
8
285Polygons that have no portions of their diagonals in the exterior are called
A. squares
B. triangles
c. convex
D. concave
8
286In the figure above (not to scale) ABCD
is trapezium in which ( overline{boldsymbol{A B}} | overline{boldsymbol{C D}}, mathbf{A D}= )
( mathrm{CD} ) and ( mathrm{AB}=2 mathrm{CD} )
If ( angle A D C=100^{circ} ) then find ( angle A B C )
A ( cdot 40^{circ} )
B .50
( c cdot 60^{circ} )
D. 70
8
28710. In the figure, find the value of x.
a
850 a
3.
In
m
V89°
8
288Plane figure with four sides is known as
( mathbf{a} )
A. Pentagon
B. Trianglel
D. none of these
8
289A rectangular paper of length ( 45 mathrm{cm} ) and
breadth ( 5 mathrm{cm} ) is cut to form a square with the same area. What is the side of
the square?
8
290In a trapezium. ABCD, ( angle A D C=110^{circ} )
Find ( angle boldsymbol{A} )
A ( .50^{circ} )
B. ( 60^{circ} )
( c .70^{circ} )
D. ( 80^{circ} )
8
291Instruments used to draw circle
A. scale and setsquare
B. scale and protractor
C. scale and compass
D. scale
8
292Prove that line segment joining the mid-
points of the diagonals of a trapezium
is parallel to the parallel sides and equal to half their difference.
8
293The vertices of a convex polygon point
are
A. outwards
B. inwards
c. middle
D. extreme corner
8
294In the above figure both RISK and CLUE are parallelograms. Find the value of ( x )8
2951.
PUUTTEL
9. Four angles of a quadrilateral are in the ratio 3:5:7:9. Find the angles.
Sol. Suppose the measure of four angles are 3x, 5x, 7x and 9r Bangla
8
2967.
In the diagram, ABCD is a rhombus.
The value of x-yis:
(a) 50°
(c) 30°
8
297( square_{0} )
0
( Delta )
8
298Two regular polygons are such that the
ratio between their number of sides is
1: 2 and the ratio of measures of their
interior angles is ( 3: 4 . ) Find the number of sides of each polygon.
8
299Prove that if the diagonals of a parallelogram are equal then it is a rectangle.8
300( A B C D ) is a rectangle with ( angle A B D= )
( 40^{circ} . ) Determine ( angle D B C )
8
301What do you call a parallelogram which has equal diagonals?
A. A trapezium
B. A rectangle
c. A rhombus
D. A kite
8
302A simple closed curve made up of only line segments is called a
A . Curve
B. Polygon
c. surface
D. concave
8
303ABCDE…… is part of a polygon which has
interior angles of ( 160^{0} . ) CDLM is a
Square.
Find the value of ( x ) and ( y ) respectively.
A. 70,105
B. 70,150
c. 105,70
D. 150,70
8
304What is the length of the other sides of
the rectangle as shown in the figure, if
side ( A B=10 ) and ( B C=7 ? )
( A cdot C D=10 ) and ( A D=5 )
B. ( C D=10 ) and ( A D=7 )
( c cdot C D=7 ) and ( A D=7 )
D. ( C D=7 ) and ( A D=10 )
0
8
305How many sides does a polygon have whose sum of the interior angles is
( 1980^{circ} ? )
A . 10
B. 13
c. 11
D. None of these
8
306If the interior angle of a regular polygon
exceeds the exterior angle by ( 132^{circ}, ) then the number of sides of the polygon is :
A . 15
B. 14
c. 13
D. 12
8
307In a given square ( A B C D, ) if the area of triangle ( A B D ) is ( 36 mathrm{cm}^{2}, ) find
(i) the area of triangle ( B C D ; ) (ii) the
area of the square ( A B C D )
8
308In the following figure, ABCD is a parallelogram.
Then find the value of ( x )
8
309If the non-parallel sides of a trapezium are equal, then it is cyclic.
A. True
B. False
8
310State true or false:
In a trapezium ( A B C D ) in which ( A B ) is
parallel to ( D C ) and ( A D=B C ), then
( angle A D C=angle B C D )
A. True
B. False
8
311In the following figures, ( A B C D ) is a
rhombus. Find the values of ( x ) and ( y )
( mathbf{A} cdot 50^{circ}, 50^{circ} )
B ( cdot 30^{circ}, 50^{circ} )
c. ( 20^{circ}, 50 )
D. None of these
8
312Show that the points
(2,-2),(8,4),(5,7) and (-1,1) taken
in order constitute the vertices of a
Rectangle.
8
313A parallelogram whose all sides are
equal is called
A. Square
B. Rhombus
c. Rectangle
D. Trapezium
8
314In the given figure, two identical regular
hexagons are placed side by side as
shown.
Find the value z.
( mathbf{A} cdot 60^{circ} )
( mathbf{B} cdot 90^{circ} )
( mathbf{C} cdot 120^{circ} )
D. ( 160^{circ} )
8
315Can it be possible that an interior angle
of a regular polygon is ( 22^{circ} ? )
A. True
B. False
c. Ambiguous
D. Data Insufficient
8
316040191
The number of measurements required to construct a
IS
8
317The angles of a pentagon in degrees are ( boldsymbol{y}^{o},left(boldsymbol{y}+mathbf{2 0}^{o}right),left(boldsymbol{y}+mathbf{4 0}^{o}right),left(boldsymbol{y}+mathbf{6 0}^{o}right) ) and
( left(y+80^{circ}right) . ) The smallest angle of the
pentagon is
( A cdot 88^{circ} )
B. ( 78^{circ} )
( c cdot 68^{circ} )
( D cdot 58^{circ} )
8
3183.
A square is a rhombus in which
A rhomhus has all its sides of
8
319in two reg
he ratio 5
between
of the poly.
53. The number of sides in two
ular polygons are in the rati
4 and the difference betw
each interior angle of the
gons is 6º. Then the number
sides are
(1) 15, 12 (2) 5, 4
(3) 10,8 (4) 20, 16
8
320The interior angles of a pentagon are in the ratio ( 4: 5: 6: 7: 5 . ) Find each angle
of the pentagon
A ( cdot 80^{circ}, 100^{circ}, 120^{circ} 140^{circ} ) and ( 100^{circ} )
( ^{circ} )
В. ( 100^{circ}, 120^{circ}, 110^{circ}, 140^{circ} ) and ( 100^{circ} )
D. none of the above
8
321( A B C D ) is a rectangle and ( P, Q, R ) and ( s )
are mid-points of the side ( A B, B C, C D )
and DA respectively. Show that the quadrilateral PQRS is a rhombus.
8
322Which of the following options shows the same property between a rectangle and a square?
A. Both have only 1 pair of parallel lines
B. Both have all the angles of measure ( 90^{circ} )
c. Diagonals cut each other perpendicularly
D. Both have all sides of equal length
8
323Match List I with List II and select the
correct answer using the codes given below the lists
8
324( A B C D ) is a parallelogram and ( A P ) and
( C Q ) are perpendiculars from vertices ( A )
and ( C ) on diagonal
BD( see Fig.). Show that ( mathbf{A P}=mathbf{C Q} )
8
325If ( A B C D ) is a parallelogram with two adjacent angles ( A ) and ( B ) equal to each other, then the parallelogram is?
A. Rhombus
B. Trapezium
c. Rectangle
D. None of These
8
326The length of one side of a
parallelogram is ( 17 mathrm{cm} ). If the length of its diagonals are ( 12 mathrm{cm} 26 mathrm{cm} ), then find
the length of the other side of a
parallelogram.
8
327If each angle of a regular polygon is
( 135^{circ}, ) how many sides does it have?
( A cdot 6 )
B. 7
( c cdot 8 )
D. 9
8
328( A B C D ) is a trapezium in which ( A B | D C ) and its diagonals intersect
each other at the point ( O . ) Show that ( frac{A O}{B O}=frac{C O}{D O} )
8
329A parallelogram whose sides are ( 10 mathrm{cm} ) and ( 5 mathrm{cm} ) has one diagonal of ( 8 mathrm{cm}, ) then the length of the other diagonal is
( mathbf{A} cdot 12 mathrm{cm} )
B. ( 11 mathrm{cm} )
( mathrm{c} cdot 14 mathrm{cm} )
D. None of these
8
330Find the area of a square whose
perimeter is ( 160 mathrm{m} . ) A floor ( 3.0 mathrm{m} ) long and ( 2.0 mathrm{m} ) wide is to be covered with
square shaped tiles of length ( 10 mathrm{cm} . ) Find
the cost of flooring it, if the cost of tiles
is Rs.150 per 100 tiles.
8
331The base angles of a issoceles trapezium are
A. unequal
B. equal
c. circular
D. diagonals
8
3324.
Which of the following is/are concave polygon?
(a) B2
(b) F
)
В
(d)
0
А
В
11.
11.
.
8
333maTCHING WIL W
U WUJU U
WUND BUILD CUUMIL-11.
Column-I
Column-II
(A) Parallelogram
(B) Rhombus
(C) Rectangle
(p) opposite sides are equal.
(9) Diagonals are equal.
(r) Diagonals bisect each
other.
(D) Square
(s) opposite angles are equal.
(t) All sides are equal.
8
334In triangle ( A B C, D ) and ( E ) are mid-
points of sides ( A B ) and ( B C )
respectively. Also, ( boldsymbol{F} ) is a point in side
( A C ) so that ( D F ) is parallel to ( B C )
Find the perimeter of parallelogram
( D B E F, ) if ( A B=10 mathrm{cm}, B C=8 cdot 4 mathrm{cm} )
and ( A C=12 mathrm{cm} )
A ( .28 .7 mathrm{cm} )
в. ( 22.5 mathrm{cm} )
c. ( 18.4 mathrm{cm} )
D. ( 18.5 mathrm{cm} )
8
335DA
In the above figure, ABCD is a square and BCE is an
equilateral triangle, what is the measure of angle DEC?
(a) 15°
(b) 30°
(c) 20°
(d) 45°
8
336the given figure lines p and q are parallel. Find value of x
so that lines land m be parallel.
m
8
337Find the ZADC, ZECF and ZEBC in the below given
figure.
8
338Diagonals of a rectangle are:
A. equal to each other
B. not equal
C. one is double of other
D. none
8
339In the figure given below ( square P Q R S ) is a
trapezium. seg ( boldsymbol{P Q}|operatorname{seg} boldsymbol{M} boldsymbol{N}| operatorname{seg} boldsymbol{S} boldsymbol{R} )
If ( boldsymbol{P} boldsymbol{M}=mathbf{8}, boldsymbol{M} boldsymbol{S}=mathbf{1 0} ) and ( boldsymbol{N} boldsymbol{R}=mathbf{5} )
then find ( Q N )
8
340Two consecutive sides of a
parallellogram are ( 4 x+5 y=0 & 7 x+ )
( 2 y=0 . ) If the equation to one diagonal
is ( 11 x+7 y=9, ) find the equation to
the other diagonal.
8
341– How many sides does a regular polygon have if each of its
interior angles is 1657
8
342Given ABCD is a parallelogram, find the
measure of ( x-2 y+z ) in degrees form
the following figure
8
343State whether True or False.
(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.
8
344Side of a square is ( 5 mathrm{cm} ). What is the
length of its diagonal.
8
345How many sides does a regular polygon have if each of its interior angles is
( mathbf{1 6} mathbf{5}^{mathbf{0}} ) ?
A. Number of sides ( =24 )
B. Number of sides= 30
c. Number of sides ( =36 )
D. Number of sides ( =42 )
8
346ABCD is a parallelogram in which ZDAB=75º and ZDBC
= 60° then ZCDB=
8
347Find ( angle C ) in the figure if ( overline{A B} | overline{D C} )8
3487.
Which quadrilateral have four sides of equal length?
(a) Rhombus
(b) Rectangle
(c) Parallelogram
(d) Square
8
349Show that the four triangles as shown in the adjoining fig. formed by diagonals and sides of rhombus are congruent.8
350The sides of a quadrilateral are produced in order. What
the sum of the four exterior angles?
8
3514.
Look at the angles in this quadrilateral. Which angle measure
is closest to 48°?
8
3521.
All regular polygons are
8
353Examine the table. (Each figure is
divided into triangles and the sum of the angles deduced from that)

What can you say about the angle sum
of a convex polygon with number of ( operatorname{sides}(n)=10 ? )
begin{tabular}{|l|c|c|c|c|}
hline Figure & & & & & \
hline side & 3 & & & & \
hline Ange sum & ( 180^{circ} ) & ( 2 times 180^{circ} ) & 5 & 6 \
hline
end{tabular}
A ( .720^{circ} )
B. ( 960^{circ} )
( c cdot 1080^{circ} )
D. ( 1440^{circ} )

8
354A figure is said to be regular if its sides are equal in length and angles are equal
in measure. Can you identity the regular quadrilateral?
8
355Perimeter of rectangle is- –
A ( .2(l times b) )
в. ( 2(l+b) )
c. ( (l times b times h) )
D. None of these
8
356In a parallelogram ( A B C D, A B=10 mathrm{cm} ) and
( A D=6 mathrm{cm} . ) The bisector of ( A ) meets DC in
E. AE and BC produced meet at F. Find the length of CF.
( A cdot 3 mathrm{cm} )
B. ( 4 mathrm{cm} )
( c cdot 5 mathrm{cm} )
( D cdot 6 mathrm{cm} )
8
357Find the measure of each angle of a parallelogram, one its angle is 30 less than twice the smaller angle.8
358Fed the measure of each angle of a parallelogram, if one of
** angles is 30° less than twice the smallest angle.
S
P2-30°
2x-30°
8
359Explain how a square is a rectangle.
Answer: A square is a parallelogram with each angle a right angle; so it is a rectangle.
A. True
B. False
8
3603.
Which of the following statement(s) is/are true?
(a) A parallelogram in which two adjacent angles are equal
is a rectangle.
(b) A quadrilateral in which both pairs of opposite angles
are equal is parallelogram.
(c) In a parallelogram, the number of acute angles is zero
or two.
(d) None of these
8
3612.
In the figure given below AN and CP are perpendiculars to
the diagonal BD of a parallelogram. Then
(a) AN=CP
(c) ANCP
(d) None of these
8
362PQRS is a parallelogram and ( angle 1 ) and ( angle 2 ) are two exterior,angles, then ( angle 1= )
( angle 2=angle 3=angle 4 )
A. True
B. False
8
363If ( A B C D ) is a parallelogram, ( A E perp )
DC and ( boldsymbol{C F} perp boldsymbol{A D} ). If ( boldsymbol{A B}=mathbf{1 6 c m} )
( A E=8 c m ) and ( C F=10 mathrm{cm}, ) find
( A D )
8
364In the pentagon ( A B C D E ) shown above,
the measures of angles ( A, E ) and ( C ) are
given. It is known that the measures of
angles ( B ) and ( D ) are equal.Then which of
the following is true?
( mathbf{A} cdot overline{A B} | overline{C D} )
( mathbf{B} cdot overline{B C} | overline{A E} )
( mathbf{c} cdot overline{A B} | overline{D E} )
D. ( overline{C D} | overline{A E} )
8
365Show that the diagonals of a
parallelogram divide it into four triangles of equal area.
8
366Position of Q is
A. Interior of curve
B. Exterior of curve
c. on the curve
can not be said
8
3674. The diagonals of a rectangle ABCD meet at O. If ZBOC
8
368Give reasons for the following. Squares, rectangles, parallelograms are all quadrilaterals.8
369The ratio of the measure of the angles in
a rhombus is ( 2: 7 . ) What is the measure
of the four angles?
В. ( 40^{circ}, 140^{circ}, 40^{circ}, 140^{circ} )
C ( cdot 65^{circ}, 115^{circ}, 65^{circ}, 115^{circ} )
D. None of the above
8
3703.
Find the angle measurex in the following figures.
50
130°
1200
609
(iv)
8
37115. The angle between the two altitudes of a parallelogram
through the vertex of an obtuse angle of the parallelogram
is 45º. Find the angles of the parallelogram.
8
372Examine the table. (Each figure is
divided into triangles and the sum of the angles deduced from that)

What can you say about the angle sum
of a convex polygon with the number of
( operatorname{sides}(n)=8 ? )
begin{tabular}{|l|c|c|c|c|}
hline Figure & & & & & \
hline side & 3 & & & & \
hline Ange sum & ( 180^{circ} ) & ( 2 times 180^{circ} ) & 5 & 6 \
hline
end{tabular}
A ( .720^{circ} )
B. ( 960^{circ} )
( c cdot 1020^{circ} )
D. ( 1080^{circ} )

8
373A square of side ( a ) lies above the ( x ) -axis
and has one vertex at the origin. The side passing through it makes an angle ( left(0<alpha<frac{pi}{4}right) ) with the positive direction of ( x ) -axis. The equation of its diagonal not through the origin
A ( cdot y(cos alpha-sin alpha)-x(sin alpha-cos alpha)=a )
B cdot ( y(cos alpha+sin alpha)+x(sin alpha-cos alpha)=a )
c. ( y(cos alpha+sin alpha)+x(sin alpha+cos alpha)=a )
D・ ( y(cos alpha+sin alpha)+x(cos alpha-sin alpha)=a )
8
374The perimeter of a rhombus is ( 100 mathrm{cm} ) and one of the diagonals is ( 40 mathrm{cm} ) Then the area of the rhombus is
A. ( 1000 mathrm{cm}^{2} )
В. ( 500 mathrm{cm}^{2} )
c. ( 1200 mathrm{cm}^{2} )
D. ( 600 mathrm{cm}^{2} )
8
375( A B C D ) is a quadrilateral in which ( A B )
and ( C D ) are smallest and longest sides
respectively.
Prove that ( angle A>angle C a n d angle B>angle D )
8
376( A B C D ) is a quadrilateral in which
( P, Q, R ) and ( S ) are mid-points of the ( operatorname{sides} A B, B C, C D ) and ( D A )
respectively. Show that ( P Q R S ) is a
parallelogram.
8
3775.
The angles of a quadrilateral are in the ratio 1:3:4:7. Find
all the angles of the quadrilateral.
8
378Identify the number of polygons from the given figures?
A . 5
B . 2
( c cdot 6 )
D. 3
8
37913. Name the quadrilaterals whose diagonals.
(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal.
C
8
380Three of the exterior angles of a hexagon are ( 40^{circ}, 51^{circ} ) and ( 86^{circ} . ) If each of
the remaining exterior angles is ( x^{circ}, ) find
the value of ( x )
A . 58
B. 61
c. 65
D. none of the above
8
381A polygon with minimum number of
sides is called as ?
A. pentagon
B. square
c. triangle
D. angle
8
382Diagonals ( A C ) and ( B D ) of a trapezium
( A B C D ) with ( A B | D C ) intersect each
other at ( O . ) Prove that ( a r(A O D)= )
( boldsymbol{a} boldsymbol{r}(boldsymbol{B O C}) )
8
383PQRS is a isosceles trapezium with
( boldsymbol{P Q} | boldsymbol{R S}, ) if ( mathrm{P}=mathbf{6 0}, ) then ( mathrm{Q} ) equals to
A . 120
B . 30
( c .60 )
D. 150
8
384The parallel sides of the trapezium are known as
(a) bases
(b) perpendiculars
(c) hypotenuse (d) none
8
385A metal box with a square base and
vertical height is to contain ( 1024 mathrm{cm}^{2} )
The material for the top and the bottom
( operatorname{costs} mathrm{Rs} .5 / mathrm{cm}^{2} ) and the material for the
sides costs Rs. ( 2.50 / c m^{2} ). Find the least
( operatorname{cost} ) of the box.
8
386A rectangular MORE is shown below:
M
Answer the following questions by giving appropriate
reason.
( IS RENOM?
(ii) Is ZMYO= ZRXE?
(1) Is ZMOY= Z REX? (iv) Is AMYO= ARXE?
(v) IS MY =RX?
8
387( A B C D ) is a trapezium in which
( A B|| C D ) and ( A D=B C . ) Show that
( angle A=angle B )
8
388If ( D, E, F ) are the mid-points of the sides ( B C, C A ) and ( A B ) respectively of ( triangle A B C, ) prove that ( B D E F ) is a parallelogram whose area is half to that
of ( triangle A B C . ) Show that ( a r(triangle D E F)= ) ( frac{1}{4} a r(triangle A B C) )
8
389How many diagonals does a regular hexagon have?
( mathbf{A} cdot mathbf{8} )
B. 9
c. 10
D. 1
8
390State true or false:
In a square ( A B C D ), diagonals meet at
O. ( P ) is a point on ( B C ) such that ( O B= )
( B P, ) then
( angle P O C=left(22 frac{1}{2}right)^{0} )
A. True
B. False
8
391Find the number of sides of a regular
polygon if each exterior angle
measures: ( 45^{circ} )
8
392&
in the diagram. ABCD is a rhombus. AFC and BED are
straight lines
p+q+r+s+t=?
(a) 2000
(c) 360°
(b) 270°
(d) 540°C
8
393Let ( A B C D E F ) be a convex hexagon in which the diagonals ( A D, B E, C F ) are
concurrent at ( O . ) Suppose the area of
triangle ( O A F ) is the geometric mean of
those of ( O A B ) and ( O E F ; ) and the area
of triangle ( O B C ) is the geometric mean
of those of ( boldsymbol{O} boldsymbol{A} boldsymbol{B} ) and ( boldsymbol{O} boldsymbol{C} boldsymbol{D} ). Prove that
the area of triangle ( O E D ) is the
geometric mean of those of ( O C D ) and
OEF.
8
394The following figures GUNS and RUNS
are parallelograms. Find ( x ) and ( y ) (Lengths are in ( mathrm{cm} ) )
8
395In the parallelogram ABCD the angles ( A ) and ( C ) are obtuse Points ( X ) and ( Y ) are
taken on the diagonal BD such that the angles ( mathrm{XAD} ) and ( mathrm{YCB} ) are right angles. And hence, ( boldsymbol{X} boldsymbol{A}=boldsymbol{Y} boldsymbol{C} )
If the above statement is true then
mention answer as 1 , else mention 0 if
false
8
396Is it possible to have a polygon whose
sum of interior angles is ( 320^{circ} ? )
A. Yes
B. No
c. Ambiguous
D. Data not sufficient
8
397In an isosceles trapezium, the length of the parallel sides, and the lengths of the non-parallel sides are all equal to ( 30 . ) In order to maximize the area of the
trapezium, the smallest angle should
be
( A cdot frac{pi}{6} )
B.
( c cdot frac{pi}{3} )
D.
8
398ms.
7.
parallel
What is the sum of exterior angles in a convex polygon?
8
399There is a regular polygon whose each
interior angle is ( 150^{circ} ) State true or false.
A. True
B. False
8
400Find the measure of interior angle. Also name the polygon.8
401A parallelogram has sides ( 6 mathrm{cm} ) and
( 4 mathrm{cm} ) and one of its diagonals is ( 8 mathrm{cm} )
then its area is :-
8
40210.
The diagonal of rectangle is thrice its smaller side. The
ratio of its sides is
8
4038.
Two adjacent angles of a parallelogram have equal measure.
Find the measure of each of the angles of the parallelogram.
UUDIS corallelograms
8
404on pnh DIO SIRuspinn
TAMA TAna
10. Opposite sides of a trapezium are parallel.
8
405A square is rectangle. Give reason8
406Find the perimeter of a rectangular hall, if its length exceeds its breadth by ( 7 mathrm{m} )
and the area of the hall is ( 228 m^{2} )
A. 72 m
в. ( 70 mathrm{m} )
( c .64 mathrm{m} )
D. ( 62 mathrm{m} )
8
407If ( A B C D ) is a rhombus such that
( angle A C B=40^{circ}, ) then ( angle A D B ) is
A ( cdot 40^{circ} )
B . ( 45^{circ} )
( c .50^{circ} )
D. ( 60^{circ} )
8
408Identify closed curve.
( mathbf{A} cdot 1 ) only
B. 2 only
C. 3 only
D. 1 and 2 only
8
409In the given figure, ABCD is a
parallelogram in which ( angle D A B=75^{circ} )
and ( angle mathrm{DBC}=60^{circ} ) then the measure of ( angle )
BDC is equal to?
( A cdot 75^{circ} )
B. ( 60^{circ} )
( c cdot 45^{circ} )
D. 55
8
410If ( P ) and ( Q ) are points of trisection of the diagonal BD of a parallelogram ABCD, ( boldsymbol{C Q} | boldsymbol{A P} )
A. True
B. False
8
411Name the polygon. Make two more examples of same type.8
412One angle of a seven-sided polygon is
( 114^{circ} ) and each of the other six angles is
( x^{circ} . ) The value of ( x ) is?
A ( cdot 114^{circ} )
B. 121
( c cdot 131^{circ} )
D. ( 151^{circ} )
8
413The angles of a pentagon in degrees are ( x, x+20, x+40, x+60 ) and ( x+80, ) then
the smallest angle of the pentagon is
( mathbf{A} cdot 50^{circ} )
B. ( 68^{circ} )
( c cdot 78^{circ} )
D. ( 85^{circ} )
8
414Illustrate, if possible the following with a rough diagram:
A closed curve that is not a polygon.
8
415In the above figure both RISK and CLUE
are parallelograms. Find the value of ( x )
8
416State true or false:
The diagonal ( B D ) of a parallelogram
( A B C D ) bisects angles ( B ) and ( D ). then
( A B C D ) is a rhombus.
A. True
B. False
8
417In the quadrilateral ( A B C D ), the diagonals ( A C ) and ( B D ) are equal and
perpendicular to each other. What type of a quadrilateral is ( A B C D ? )
A. A square
B. A parallelogram
c. A rectangle
D. A trapezium
8
418The area of a rhombus is ( 28 m^{2} . ) If its
perimeter is ( 28 mathrm{m} ), find its altitude.
8
4194.
In parallelogram PQRS, O is the mid point of SQ. Find ZS
ZR, PQ, QR and diagonal PR.
s 15cm R
11cm
6 cm
1600
AZ
8
420The sum of the measures of interior
angles of a polygon of ( n ) sides is equal to
A. ( 2 n ) right angles
B. ( (2 n-2) ) right angles
c. ( 2(n-2) ) right angles
D. ( 2(n-4) ) right angles
8
421( A B C D ) is a trapezium in which ( A B ) is
parallel to ( D C ). If the diagonals
intersect at ( O ), then which one of the
following is correct?
A ( cdot frac{O A}{O C}=frac{O B}{O D} )
в. ( frac{A D}{B C}=frac{A B}{D C} )
c. ( frac{O B}{O C}=frac{B C}{C D} )
D. ( frac{O A}{D C}=frac{D A}{D C} )
8
422( P ) and ( Q ) are any two points lying on the
sides ( D C ) and ( A D ) respectively of a
parallelogram ( A B C D . ) Show that ( boldsymbol{a r}(boldsymbol{A P B})=boldsymbol{a r}(boldsymbol{B Q C}) )
8
423( A B C D ) is a square, ( X ) and ( Y ) are points
on sides ( A D ) and ( B C ) respectively, such that ( A Y=B X . ) Prove that.
( angle B A Y=angle A B Y )
8
424In a rhombus PQRS, PR = 24 cm and QS
( =18 mathrm{cm} . ) Find the perimeter of the rhombus.
8
4255. Find the measure of each exterior angle of a regular polygon
of
(
9 sides
(11)
15 sides
8
4263.
three line segments.
In which condition a polygon is called a regular polygon?
The sides of quadrilateral arenroduced in order What is
8
42759. Each internal angle of regu-
lar polygon is two times its
external angle. Then the num-
ber of sides of the polygon is :
(1) 8
(2) 6
(3) 5
(4) 7
8
428In Fig, ABCD is a parallelogram in which ĐDAB = 75°.
ĐDBC = 60° then the value ofĐCDB and ĐADB is 12k.
Find the value of k.
750
8
429110 ausunu
If the diagonals of a parallelogram bisect each other at right
angles, then it is a
8
430The measure of two adjacent angles of a parallelogram are
in the ratio 3:2. Find the measure of each of the angles of
the parallellogram.
tonalen of parallelogram have equal measure
8
431( A B C D ) is a rectangle such that ( A C+ )
( A B=5 A D ) and ( A C-A D=8, ) then
the area of rectangle ( A B C D ) is
A . 36sq. units
B. 50. sq. units
c. 60 sq. units
D. cannot be found
8
432The number of sides of two regular
polygons ( A ) and ( B ) are in the ratio 1: 3.1
each interior angle of polygon ( mathrm{B} ) is ( 168^{circ} ) find each interior angle of polygon ( boldsymbol{A} )
A ( .144^{circ} )
B. 124
( c cdot 134^{circ} )
D. none of the above
8
4332.
Assertion : A polygon having 16 sides is called 16 sider
polygon or 16-gon.
Reason: A polygon bounded by n-line segments is called
n-sides polygon or n-gon.
A contin
u emile.
-1
8
434Given are some figures. Classify each of
these figures on the basis of the following:
(i) simple curve
(ii) simple closed curve (iii) polygon
(iv) Convex polygon
(iv) convex polygon
(v) concave polygon
(vi) Not a curve
8
435a
The measure of Z A and Bis
(a) 1159.650
(b) 100°, 180°
(c) 950.850
(d) 750, 1059
8
436( A B C D ) is a parallelogram and ( P ) is a
point on the segment ( overline{A D} ) dividing it internally in the ratio 3: 1 the line ( overline{B P} )
meets the diagonal ( overline{A C} ) in ( Q . ) Then the
ratio ( boldsymbol{A} boldsymbol{Q}: boldsymbol{Q} boldsymbol{C} ) is
A .3: 4
B. 4: 3
c. 3: 2
D. 2 : 3
8
437If ( A M ) and ( C N ) are perpendiculars on
the disgonal ( B D ) of a parallelogram
( A B C D, ) Is ( triangle A M D cong triangle C N B ? ) Give
reason
8
438Determine the number of sides of a
polygon whose exterior and interior angles are in the ratio 1: 5
8
4392.
A parallelogram which has equal diagonals is a
(a) Square (b) Rectangle
(c) Rhombus (d) None
8
440A quadrilateral in which both pairs of opposite sides are parallel is a
A . square
B. rhombus
c. rectangle
D. parallelogram
8
441Let ABCD be a parallelogram. The diagonals bisect in E.
(i) If ( A B=6 mathrm{cm} ) and ( A D=4 mathrm{cm}, ) find ( C D )
and BC.
(ii) If ( mathrm{DE}=5 mathrm{cm} ) and ( mathrm{AE}=7 mathrm{cm}, ) find ( mathrm{BD} )
and AC.
(iii) If ( angle D A B=72^{circ}, ) find the measure
of ( angle C B A )
( (text { iv ) If } boldsymbol{A} boldsymbol{D}=(boldsymbol{x}+boldsymbol{2} boldsymbol{y}), boldsymbol{B} boldsymbol{C}=(boldsymbol{2} boldsymbol{x}+ )
( mathbf{3}), boldsymbol{D} boldsymbol{C}=(boldsymbol{x}+boldsymbol{7}) ) and ( boldsymbol{A} boldsymbol{B}=(boldsymbol{3} boldsymbol{y}+boldsymbol{2}) )
find ( A B ) and ( B C ).
8
442In the given five sided closed figure,
find ( angle boldsymbol{E} boldsymbol{A} boldsymbol{B}+angle boldsymbol{A} boldsymbol{B} boldsymbol{C}+angle boldsymbol{B} boldsymbol{C} boldsymbol{D}+ )
( angle C D E+angle D E A )
( 4 cdot 520 )
B. ( 540^{circ} )
( c .530 )
D. 140
8
44367. The ratio between the number of
sides of two polygon is 2:1 and
the ratio between their interior
angle is 4 : 3. The number of
sides of these polygons are re-
spectively:
(1) 8,4 (2) 10,5
(3) 12,6 (4) 14,7
8
444The four angles of a quadrilateral are equal. Draw this quadrilateral in your notebook. Find each of them.8
445In a parallelogram ( mathrm{ABCD}, angle B=(2 x+ )
25)( ^{0} ) and ( angle D=(3 x-5)^{0} . ) Find:
(i) The value of ( x )
(ii) Measure of angle.
B. ( x=32, b=91 ) degrees, de ( =89 ) degrees
c. ( x=30, b=89 ) degrees, d=91 degrees
D. ( x=32, b=89 ) degrees, d=91 degrees
8
446ABCD is a quadrilateral. If ( A C ) and ( B D ) bisect each other then ABCD must be a
A. triangle
B. cylinder
c. parallelogram
D. pyramid
8
447( A B C D ) is a quadrilateral in which all four sides are equal. Show that both
pairs of opposite sides are parallel.
8
448A polygon which has no diagonal.
B. Heptagon
c. Triangle
D. Pentagon
8
4493.
IfBC = 5 cm, then AD=
(a) 5cm
c) 6 cm
(b) 4.8 cm
(d) none of these
8
450Classify the following curve as open or
closed
8
451If ( A B C D ) is a parallelogram and ( E, F )
are the centroids of ( triangle A B D ) and ( B C D )
respectively, then ( boldsymbol{E} boldsymbol{F} ) equals
( mathbf{A} cdot A E )
в. ( B E )
c. ( C E )
D. ( D E )
8
4522. Match the column:
Column-I
Column-II
(A) ABCDE is a regular pentagon. (p) 70°
The bisector of Z A of the
pentagon meets the side CD in M.
Then Z AMC is
(B) The angles of a quadrilateral are
(q) 80°
respectively equal to 1109,50° and
40°. The fourth angle is.
(C) In a quadrilateral ABCD, the bisector (r) 90°
of Z A and B meet at point P. If
ZC=100°, ZD=60°, the mZ APB is
(D) Three angles of a quadrilateral are (s) 160°
equal: Fourth angle is of measure
150°. The measure of equal angles is
8
453The figure obtained by joining the midpoints of the adjacent sides of a rectangle of sides ( 8 mathrm{cm} ) and ( 6 mathrm{cm} ) is
A . a rectangle of area ( 24 mathrm{cm}^{2} )
B. a square of area ( 25 mathrm{cm}^{2} )
c. a rhombus of area ( 24 mathrm{cm}^{2} )
D. a trapezium of area ( 12 mathrm{cm}^{2} )
8
454f PQRS is a square, ( A B | S Q ) and
( A C=C B, ) which one is true?
A ( . S A=B Q )
B. PC is the bisector of ( angle S P Q )
c. PC if produced will pass through
D. All of these
8
455Each interior angle of regular polygon is 144º. Find the
interior angle of a regular polygon which has double the
number of sides as the first polygon.
11 lorom if one of
8
456Find the number of sides of a regular polygon whose each exterior angle has a
measure of:
( 45^{circ} )
8
457( boldsymbol{A}(mathbf{5}, mathbf{7}), boldsymbol{B}(mathbf{4}, mathbf{1 2}), boldsymbol{C}(mathbf{9}, mathbf{1 1}) ) and ( boldsymbol{D}(mathbf{1 0}, mathbf{6} )
are four points. Show that ( A B C D ) is a
rhombus
8
4583.
8
4591.
Assertion : A quadrilateral can be constructed if at least
any five independent elements are given.
order to be sufficient must also satisfy (i) the
triangle inequality and (ii) angle sum property
of a triangle, wherever applicable.
8
4602.
Given hore are some figures
(Ν)
ΣΟΟΡΙΑ
(vi)
Classify each of them on the basis of the following.
(a) Simple curve
(b) Simple closed curve
(c) Polygon
(d) Convex polygon
(e) Concave polygon
wing figures.
8
461The side of a rhombus in ( 5 mathrm{cm} ). If the
length of one diagonal of the rhombus is
( 8 mathrm{cm}, ) then find the length of the other diagonal.
8
462If the sum of all the angles of a polygon except one angle is ( 2220^{circ}, ) then the number of sides of the polygon is
A . 12
B. 13
( c cdot 14 )
D. 15
8
463If ( boldsymbol{A}(-2,1), B(a, b), C(4,6) ) and ( D(1,2) )
are the vertices of parallelogram. Find
( a+b )
8
464The measurement of each angle of a
polygon is ( 160^{circ} . ) The number of its sides
is?
A . 15
B. 18
c. 20
D. 30
8
465Four angles of a polygon are ( 120^{circ} ) each
and the remaining angles are all equal
to ( 160^{circ} ) each. Find the number of sides
8
466UUUUUUUULI
5.
The diagonals of a rhombus bisect
8
467ABCDE is regular pentagon. The bisector
of ( angle A ) of the pentagon meets the side
CD in M. Then the measure ( angle A M C ) is
A ( .54^{circ} )
B . ( 45^{circ} )
( c cdot 90^{0} )
D. ( 100^{circ} )
8
468The bisectors of angles of a
parallelogram makes a figure which is
A. rectangle
B. circle
c. pentagon
D. octagon
8
469Assertion : In a parallelogram if one angle is a right angle,
then it is called a rectangle.
Reason: In a rectangle if all the sides are equal then it is
called a square.
8
470If ( A B C D ) is a parallelogram whose diagonals intersect at ( O ) and ( triangle B C D ) is
an equilateral triangle having each side of length ( 6 mathrm{cm} ), then the length of diagonal ( boldsymbol{A C} ) is
A ( cdot 2 sqrt{3} mathrm{cm} )
B. ( 6 sqrt{3} mathrm{cm} )
c. ( 3 sqrt{6} mathrm{cm} )
D. ( 12 mathrm{cm} )
8
471Draw rough diagrams to illustrate the following:
(a) Open curve
(b) Closed curve
8
472In a trapezium pqrs with ( boldsymbol{P Q} | boldsymbol{S} boldsymbol{R} ) the
diagonals ( P R ) and ( Q S ) intersect at ( x ) if ( P Q=frac{2}{3} R S . ) Find the ratio of areas of
triangles ( P R Q ) and ( R X S )
8
473Two sticks each of length 7 cm are crossing each other
such that they bisect each other at right angles. What shape
is formed by joining their end points? Give reason.
8
474Find the sum of interior angles of a
polygon with 8 sides.
8
475( A B C D ) is a trapezium with ( A B / / D C ) A line parallel to ( A C ) intersects ( A B ) at
point ( M ) and ( B C ) at point ( N . ) Prove that area of ( triangle A D M= ) area of ( triangle )
( A C N )
8
476Show that (-3,2),(-5,-5),(2,-3)
and (4,4) are the vertices of a rhombus.
8
477Prove that in a parallelogram the opposite angles are equal.8
4786.
Can a quadrilateral ABCD be a parallelogram if
() ZD+ ZB=180°?
() AB=DC=8 cm, AD=4 cm and BC=4.4 cm?
(iii) ZA= 70° and ZC=65°?
8
4794. Find the number of sides of a regular polygon whose each
exterior angle has a measure of 45°.
8
4806.
9. In a quadrilateral PQRS; P= 70°, 20=90°; ZR=55°
Find the measure of ZS. What kind of quadrilateral is it?
Convex or concave.
1
8
481ABCD is a parallelogram in which ZDAO = 40
BAO = 35º and ZCOD = 65°. Find ZODC.
650
R350
8
482In the figure, diagonals ( A C ) and ( B D ) of
quadrilateral ( A B C D ) intersect at ( O )
such that ( O B=O D ), show that
( a r(Delta D O C)=a r(Delta A O B) )
8
483A chord is ( 8 mathrm{cm} ) away from the centre of
a circle of radius ( 17 mathrm{cm} . ) Find the length
of the chord.
8
484The diagonal of a rectangle whose length is ( 20 mathrm{cm} ) and breadth in ( 15 mathrm{cm} ) is
( mathbf{A} cdot 35 mathrm{cm} )
B. ( 30 mathrm{cm} )
c. ( 25 mathrm{cm} )
D. ( 40 mathrm{cm} )
8
485What is the name of the quadrilateral which can be drawn
from the given data?
(a) square
(b) Rhombus
(c) Parallelogram
(d) Rectangle
8
486In which quadrilateral all sides and
angles are equal?
A. rectangle
B. parallelogram
c. square
D. kite
8
487A rhombus is symmetrical across –
A. its diagonals
B. its vertices
( mathrm{C} ). its sides
D. its angles
8
488In a trapezium ( A B C D ) with ( A B | C D ), it
is given that ( A D ) is not parallel to ( B C ).
Is ( triangle A B C cong triangle A D C ? ) Given reasons
8
489State and draw the lines of symmetry for a rhombus.8
490Give Reason:
A square can be thought of as a special
rhombus.
8
4913.
Assertion : In a regular polygon,
i all sides are equal
(ii) all interior angles are equal
(i) all exterior angles are equal.
Reason: A polygon is called regular polygon if all its sida
as well as angles are equal.
8
4921.
Write the angle-sum property of a quadrilateral.
ome of the polygon which is bounded
8
49371. If the sum of interior angles of a
regular polygon is equal to two
times the sum of exterior angles
of that polygon, then the num-
ber of sides of that polygon is
(1) 5
(2) 6
(3) 7
(4) 8
8
494Classify the following curve as open or
closed
8
495( A B C D ) is a rectangular and ( P, Q, R )
and ( S ) are mid points of the sides ( A B, B C, C D ) and ( D A ) respectively. Show that the quadrilateral ( P Q R S ) is a
rhombus.
8
496Identify open curve.
( mathbf{A} cdot 1 ) only
B. 2 only
( mathrm{C} cdot 1,2 ) only
D. 3only
8
497Formula for
polygon is ( (boldsymbol{n}-mathbf{2}) times mathbf{1 8 0}^{boldsymbol{o}} )
A. sum of exterior angles
B. sum of interior angles
c. number of edges
D. number of diagonals
8
( A B C D, angle O C D=30^{circ} . ) Calculate
( angle B O C . ) What type of triangle is ( B O C ? )
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499Name the polygon. Make two more
examples of same type.
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500( A B C D ) is a rectangle in which diagonal
( A C ) bisects ( angle A ) as well as ( angle C . ) Show
that:
(i) ( A B C D ) is a square
(ii) diagonal ( B D )
bisects ( angle B ) as well as ( angle D )
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501ABCD is a parallelogram as shown in figure. If ( A B=2 A D ) and ( P ) is mid-point of
( A B, ) then ( angle C P D ) is equal to
( A cdot 90^{circ} )
B. ( 60^{circ} )
( c cdot 45^{circ} )
D. ( 135^{circ} )
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50214. ABC is a right-angled triangle and O is the mid point of the
side opposite to the right angle. Explain why O is equidistant
from A, B and C. (The dotted lines are drawn additionally to
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503The angle of a pentagon are in the ratio ( 4: 8: 6: 4: 5 . ) Find the greatest angle of
the pentagon.
( mathbf{A} cdot 120^{circ} )
B. ( 140^{circ} )
( c cdot 160^{circ} )
D. 150
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504Find the number of sides of regular polygon whose measure of each of its interior angle is ( frac{360^{circ}}{7} )
( A cdot 7 )
B. 8
c. 9
D. 6
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505( ln ) a hexagon ( A B C D E F ; ) side ( A B ) is
parallel to side ( boldsymbol{F} boldsymbol{E} ) and ( angle boldsymbol{B}: angle boldsymbol{C}: angle boldsymbol{D} )
( angle E=6: 4: 2: 3 )
Find the measure of ( angle B )
( mathbf{A} cdot 108 )
B . ( 216^{circ} )
( c cdot 244^{circ} )
D. None of these
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506State the name of a regular polygon of 4 sides.
A. Square
B. Trapezium
c. Rectangle
D. Parallelogram
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507What is the name given to a parallelogram whose all sides are equal
( ? )
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508Find the number of sides of a regular
polygon if each exterior angle is equal to its adjacent interior angle
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509See the figure above
Find its perimeter.
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510Two regular polygons are such that the ratio between their number of sides is
1: 2 and the ratio of measure of their
interior angles is ( 3: 4 . ) The number of
sides of each polygon is
A . 5,10
B. 6, 12
c. 4,8
D. 2,3
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511Find the length of a chord which is at a
distance of ( 15 mathrm{cm} ) from the centre of a
circle of radius ( 25 mathrm{cm} )
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5121.
The diagonals of a rectangle ABCD intersect in O. If
ZBOC=68°, find Z ODA.
D
68°
:
121
f ZBAN
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513Number of measurements required to
construct a square are
A.
B. 2
( c cdot 3 )
( D )
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514Let ( A_{0}, A_{1}, A_{2}, A_{3}, A_{4}, A_{5} ) be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths
of the line segments ( A_{0} A_{1}, A_{0} A_{2} ) and
( boldsymbol{A}_{0} boldsymbol{A}_{4} ) is:
A ( cdot frac{3}{4} )
B. ( 3 sqrt{3} )
( c cdot 3 )
D. ( frac{3 sqrt{3}}{2} )
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515If the sum of all interior angles of a
polygon is ( 3240^{circ}, ) how many sides has
the polygon?
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