# Lines And Angles Questions

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

Question NoQuestionsClass
1n figure, ( A B, C D ) and ( E F ) are three
parallel lines. If ( 4 y=5 x ) and ( z=y-30 )
find ( angle q )
( A cdot 120 )
В. ( 110^{circ} )
( c cdot 100 )
D. 90
7
2In the given figure two lines ( A B ) and
( C D ) intersect at ( O . O E ) is any ray such
that ( angle B O E=80^{circ} . ) If ( angle B O D=30^{circ} )
then the find ( angle E O C )
9
3Find the complement of the angle :
( frac{1}{4} ) of a right angle
( mathbf{A} cdot 67 cdot 5^{circ} )
B ( .57 cdot 5^{circ} )
( mathbf{c} cdot 37 cdot 5^{circ} )
D. none of the above
7
4Find the supplement of the following
angle
( mathbf{1 2 0}^{circ} )
7
5State true or false:
If angles forming a linear pair are of equal measure, then each of these
angles is of measure ( 90^{circ} )
A. True
B. False
9
6Show that difference of any two sides of
a triangle is less than to the third side.
9
7An angle is ( 14^{circ} ) more than its
complementary angle, then angle is:
( A cdot 38^{circ} )
B. ( 52^{circ} )
( c .50^{circ} )
D. none of these
7
8If ( A, B ) are complementary angles, then ( cos ^{2} A+cos ^{2} B )7
9Find the angle which is supplementary of itself7
10In the given figure, ( p | q ) and ( r | s . ) Find
the values of ( x, y ) and ( z )
7
11Find the angle which is ( 56^{circ} ) more than
its complement
A . 73
B. 83
c. 45
D. 68
7
12If the given figure, AB II CD. then
( B P O+P O Q+D Q O ) is
4
3.90
( c cdot 180 )
D. ( 360^{circ} )
7
13Fill in the blanks so as to make the
following statements true:
A ray stands on a line, then the sum of the two adjacent angles so formed is
9
14In the given figure, ( angle theta ) is less than one-
third of a right angle, then:
A ( cdot phi>150^{circ} )
B ( cdot phi geq 150^{circ} )
c. ( phi leq 150^{circ} )
D. ( phi<150^{circ} )
9
15If the sides of a triangle are produced, then the sum of the exterior angle i.e. ( angle a+angle b+angle c ) is equal to
A ( .180^{circ} )
В. ( 360^{circ} )
( c cdot 90^{0} )
D. ( 270^{circ} )
9
16If ( P Q ) and ( R S ) intersect at point ( T, ) such
that ( angle P R T=40^{circ}, angle R P T=95^{circ} ) and
( angle T S Q=75^{circ} . ) Find ( angle S Q T )
9
17In the adjoining figure, the arms of two
angels are parallel, if ( angle A B C=70^{circ}, ) find
( (i) angle D G C(i i) angle D E F )
7
18The straight lines ( A B ) and ( C D ) intersect
at ( E . ) If ( E F ) and ( E G ) are bisectors of
( angle D E A ) and ( angle A E C )
respectively and if ( angle A E F=x ) and
( angle A E G=y, ) then
A ( cdot x+y>90^{circ} )
В . ( x+y<90^{circ} )
c. ( x+y=90^{circ} )
D. ( x+y=180^{circ} )
7
19Which two angles are supplementary?
A. ( angle C O F ) and ( angle A O C )
B. ( angle C O F ) and ( angle C O E )
( mathrm{c} . angle mathrm{COF} ) and ( angle E O D )
D. ( angle C O F ) and ( angle A O E )
7
20In the given figure, ( A B | C D ) and
( boldsymbol{E F} perp boldsymbol{C D} ) and ( angle boldsymbol{G} boldsymbol{E C}=mathbf{1 3 2}^{boldsymbol{o}} . ) Find
( angle boldsymbol{E} boldsymbol{G} boldsymbol{F} )
A ( cdot 43^{circ} )
B. ( 42^{circ} )
( c cdot 48 )
( D cdot 44^{circ} )
7
2153. In a A ABC, if ZA = 120° and
AB = AC, then ZB is equal to
(1) 35° (2) 60°
(3) 30° (4) 80°
9
22State True or False.
figure, ( angle P Q R=angle P R Q ), then
( angle P Q S=angle P R T )
4. True
3 falss
9
23The angle that is three times as large as its complement is:
( mathbf{A} cdot 135 )
в. 67.5
( c cdot 50.5 )
D. 45
7
24Measure of ( angle A ) in triangle ( Delta A B C ) is
( A cdot 30^{circ} )
B. ( 15^{circ} )
( c cdot 20^{circ} )
D. ( 180^{circ} )
9
25In the figure, ( Delta P Q R ) is a right angled at
( mathrm{Q}, bar{M} L | bar{R} Q ) and ( angle L M R=130^{circ} . ) Find
( angle L P M ) and ( angle P M L )
9
26Calculate the followings.
An angle is equal to one third of its supplement. Find its measure.
2
If an angle is ( 30^{circ} ) more than one half of its
complement, find the measure of the angle.
9
27Mark the correct alternative of the
following.
The angles of a triangle are in the ratio ( 2: 3: 7 . ) The measure of the largest angle is?
( A cdot 84^{circ} )
B. ( 91^{circ} )
( c cdot 105 )
D. ( 98^{circ} )
9
28In. triangle ( A B C, angle A+angle B=144 ) and ( angle A+ )
( angle C=124 )
Calculate smallest angle of the triangle.
( A cdot 36^{circ} )
B. ( 56^{circ} )
( c cdot 46^{circ} )
D. none of these
9
29Find the values of the unknown ( x ) and ( y )
in the following diagram
9
30If two supplementary angles are in the ratio ( 4: 5, ) then the angles are
A. ( 80^{circ}, 100^{circ} )
в. ( 85^{circ}, 95^{circ} )
c. ( 40^{circ}, 50^{circ} )
D. ( 60^{circ}, 120^{circ} )
7
31In the adjoining figure, identify the pair of alternate interior angles.9
32Find ( frac{boldsymbol{x}+boldsymbol{u}+boldsymbol{y}+boldsymbol{z}}{mathbf{5 0}} )9
33n ( Delta P Q R S ) is a point on ( P Q ) such that
( mathrm{SR}=mathrm{QR}=mathrm{SP} . ) and ( angle P S R=120^{circ} . ) Find
( angle P )
9
34In figure, write down each pair of
vertically opposite angles
9
35If two intersecting lines are intersected by a transversal, then corresponding angles are equal.
A. True
B. False
c. Ambiguous
D. Data Insufficient
7
36n figure, OA and OB are opposite rays if
( x=25^{circ}, ) what is the value of ( y ? )
9
37If an angle is eight times its complementary angle, then the measurement of the angle is:
A ( .90^{circ} )
B . 20
( c .80 )
D. 160
7
38In a right triangle the two acute angles are in the ratio ( 7: 11 . ) Find the measure
of acute angles.
9
39f ( boldsymbol{P Q perp P S}, boldsymbol{P Q} | boldsymbol{S R}, angle boldsymbol{S O R}=mathbf{2 8}^{boldsymbol{o}} )
and ( angle Q R T=65^{circ}, ) then find ( x & y )
9
40Indicate which pairs of angles are:
Vertically opposite angles.
( A cdot 184 )
( B cdot 2 & 4 )
( c cdot 1 & 3 )
( D cdot 5 & 4 )
9
41In the below figure ( A B, C D ) and ( E F ) are
three lines concurrent at ( O ). Find the
value of ( y )
7
42In given figure find ( x )
( mathbf{A} cdot 110^{0} )
( mathbf{B} cdot 120^{0} )
( mathbf{c} cdot 130^{circ} )
D. ( 140^{circ} )
9
43Find the measure of an angle, if four
times of its complement is ( 12^{circ} ) more
than twice the difference between its
supplement and complement.
A . 36
B . 45
c. 42
D. 24
7
44Two supplementary angles are in the ratio ( 5: 7 . ) Find the smallest angle.
[
begin{array}{l}
1^{s t} text { angle }=frac{5}{12} times 180^{circ} text { and } \
2^{n d} text { angles }=frac{7}{12} times 180^{circ}
end{array}
]
( mathbf{A} cdot 80 )
B. 75
c. 65
D. 90
7
4561. The angle in a semi-circle is
(1) a reflex angle
(2) an obtuse angle
(3) an acute angle
(4) a right angle
7
46What is the value of ( a-b )
A ( cdot 180^{circ} )
B ( .60^{circ} )
( c cdot 70^{circ} )
( D cdot 120 )
9
47Angles forming a linear pair can both be acute angles.
A. True
B. False
c. Ambiguous
D. Data Insufficient
9
48Define adjacent angle.9
49Find ( x, y, z )9
50In the adjacent figure, ABC is a triangle
in which ( angle B=50^{circ} ) and ( angle C=70^{circ} )
Sides ( A B ) and ( A C ) are produced. If ‘ ( z^{prime} ) is
the measure of the angle between the
bisectors of the exterior angles of
formed, then find ‘z’.
9
51In a ( triangle A B C, angle A-angle B=30^{circ} ) and ( angle B- )
( angle C=42^{circ} ; ) find ( angle A )
A ( cdot 84^{circ} )
B. ( 94^{circ} )
( c cdot 32^{0} )
D. none of the above
9
52Write all pairs of angles of linear pair.9
53Write the complement (in degree) of
each of the following angles: ( 30^{circ} )
7
54Find the value of unknown ( x ) in the
following diagram.
9
55Find the complementary of the angle
( mathbf{3 0}^{circ} )
7
56Find the value of the unknown interior
angle ( x ) in the following figure.
9
57Consider the following statements:
When two straight lines intersect,
(i) adjacent angles are complementary
(ii) adjacent angles are supplementary
(iii) opposite angles are equal
(iv) opposite angles are
supplementary
( A cdot ) (i) and (iii)
B. (ii) and (iii)
c. (i) and (iv)
D. (ii) and (iv)
7
58Two parallel lines ( l ) and ( m ) are cut by a
transversal ( t . ) If the interior angles of the
same side of ( t ) are ( (2 x-8)^{circ} ) and ( (3 x- )
7)( ^{circ}, ) find the measure of each of these
angles.
9
59The angle between the internal bisector and the external bisector of an angle is:
( mathbf{A} cdot 60 )
B. 90
( c cdot 120 )
D. 135
7
60In the following figure, ( A B C D ) and
PORS are two parallelograms such
that ( angle D=120^{circ} ) and ( angle Q=70^{circ} . ) Find the
value of ( boldsymbol{x} )
9
61State True or False
From the following figure, we can say:
( angle A C D=angle C B E )
( 4 . ) True
3. Falss
9
62In the figure, if ( angle B O C=7 x+20^{circ} ) and
( angle C O A=3 x, ) then the value of ( x ) for
which ( A O B ) becomes a straight line is:
( 4 cdot 16^{circ} )
B. 14
( c cdot 20 )
D. ( 21^{circ} )
7
63n given figure the value of ( x ) is :
( mathbf{A} cdot 120^{circ} )
B. ( 110^{circ} )
( c cdot 80^{c} )
D. ( 100^{circ} )
9
64In Fig. sides ( P Q ) and ( R Q ) of ( Delta P Q R ) are
produced to points ( S ) and ( T )
respectively. If ( angle S P R=135^{circ} a ) and
( angle P Q T=110^{circ} . ) Find ( angle P R Q )
9
65How many pair of vertically opposite
angles are formed?
9
66Find the value of ( x )9
67From the given figure, find :
( angle A C B )
( mathbf{A} cdot 70^{circ} )
B. ( 80^{circ} )
( c cdot 75^{circ} )
D. none of the above
9
68Find the measure of the complementary
angle of each of ( 20^{circ} )
( mathbf{A} cdot 50^{circ} )
B. ( 70^{circ} )
( c cdot 160^{circ} )
D. ( 80^{circ} )
7
69If two supplementary angles have equal measure, what is the measure of each
angle?
7
70Two adjacent angles whose sum is ( 180^{circ} ) is called
A. complementary angles
B. linear pair
c. vertically opposite angles
D. none
9
71Identify the following pairs of angles are complementary or supplementary:
( 80^{circ}, 10^{circ} )
7
72If two parallel lines are intersected by a transversal, then prove that bisectors of the interior angles from a rectangle.9
7314. Find the measure of an angle if seven times its complement
is 10° less than three times its supplement.
7
74If one angle of a triangle is ( frac{pi}{4} ) and other
angle is ( 90^{circ} ) then find the third angle in
degree measure.
7
75n figure, find the values of ( x, y ) and ( z )
( mathbf{A} cdot x=155^{circ} )
B . ( y=25^{circ} )
( mathbf{c} cdot z=155^{circ} )
D. All of these
9
76In the given figure, ( A B C ) is a triangle,
side ( mathrm{CB} ) is produced to ( mathrm{E} ) and ( angle boldsymbol{A}: angle boldsymbol{B} )
( angle C=2: 1: 3 . ) Find ( angle D B E, ) if DB is
perpendicular to AB.
A ( cdot 66^{circ} )
B . ( 46^{circ} )
( c cdot 60^{circ} )
D. none of the above
9
77In the Fig. lines ( P Q ) and RS intersect each other at point ( 0 . ) If ( angle P O R )
( angle R O Q=5: 7, ) Find all the angles
9
78From the following figure, can we say
that ( boldsymbol{A B}>boldsymbol{C D} )
If true then enter 1 else enter 0 .
9
79Find the angles in a straight line9
80A transversal intersects two parallel
lines. if the measure of one of the angle is ( 50^{0} ), then the measure of its
corresponding angle is
A ( cdot 40^{circ} )
B. ( 130^{circ} )
( c cdot 180^{circ} )
D. ( 50^{circ} )
9
81Find the value of the unknown interior
angle ( x ) in the following figure.
9
82( Delta A B C ) is a right angled at ( A, ) the value
of ( tan B times tan C ) is:
( A cdot O )
B.
( c cdot-1 )
D. None of the above
9
83In the figure ( l / / m ) and ( p ) is a
transversal, find the value of ( x, ) giving
necessary reasons.
9
84In figure,prove AB ( | mathrm{EF} )7
85In figure, ( A, B, C ) are collinear points.
Name two linear pairs.
9
86Prove that the sum of angles of a
triangle is 180
9
87Find ( x ) in the following figure ( (A B | C D) )9
88In figure, lines ( X Y ) and ( M N ) intersect at 0
If ( angle P O Y=90^{circ} ) and ( a: b=2: 3, ) find ( c )
( 4 cdot 106 )
B. ( 156^{circ} )
( c cdot 126^{circ} )
D. 136
9
89( angle A ) and ( angle B ) are supplementary angles.
( angle A=x+10^{circ} ) and ( angle B=x-10^{circ}, ) find
( angle A ) and ( angle B )
7
90Find the values of the unknown ( x ) and ( y )
in the following diagram
9
91Find the complementary angle of ( 60^{circ} )7
92Find the complement of each of the
following angles:
7
93Two complementary angles differ by ( 10^{circ} ) Find the angles7
94In figure, ( angle P O R=a^{circ} ) and ( angle Q O R=b^{circ} )
If ( a^{circ}-b^{circ}=60^{circ} . ) Find angle ( a^{circ} ) and ( b^{circ} )
A ( . angle a=70^{circ}, angle b=110^{circ} )
В. ( angle a=90^{circ}, angle b=90^{circ} )
C . ( angle a=120^{circ}, angle b=60^{circ} )
D. ( angle a=60^{circ}, angle b=120^{circ} )
7
95By simply looking at the pair of angles
given in figure. State which of the angle in the pairs is greater.
9
96Write the supplement of each of the
following angles: ( 138^{circ} )
7
97Find the angle, if its complement is one-
fourth of its supplement.
7
98p and q are straight lines. If ( angle a= )
( angle boldsymbol{b}=angle boldsymbol{c}=angle boldsymbol{d}, ) find ( angle boldsymbol{a} )
( mathbf{A} cdot 97^{circ} )
B ( .49 .5^{circ} )
( mathbf{c} cdot 19.4^{circ} )
D ( .24 .25^{circ} )
9
99n Fig. if ( boldsymbol{A B} | boldsymbol{D} boldsymbol{E}, angle boldsymbol{B A C}=mathbf{3 5}^{circ} ) and
angleC ( D E=53^{circ}, ) find ( angle D C E )
9
100If true then enter 1 and if false then
enter 0

Can two acute angles form a linear pair?

9
101In the figure if ( B D | E F ), then ( angle C E F ) is:
( A cdot 100^{circ} )
B. 120
( c cdot 140 )
D. 160
7
102n fig. ( 1, ) AOB is a straight line, the value
of ( x ) is :
( A cdot 60 )
B. 30
( c cdot 20 )
( D )
7
103n the figure ( angle boldsymbol{P}+angle boldsymbol{Q}+angle boldsymbol{R}+angle boldsymbol{S}+ )
( angle boldsymbol{T}=boldsymbol{2} ) right angles
( 4 . ) True
3. Falss
9
104Find ( x ) in the following figures:9
105The measure of angle ( y ) in the given
figure is
A. ( angle y=65^{circ} )
B . ( angle y=85^{circ} )
c. ( angle y=75^{circ} )
D. ( angle y=80^{circ} )
9
106Find the measure of the supplementary
angle of ( 54^{circ} )
A ( cdot 26^{circ} )
B . ( 126^{circ} )
( c cdot 34^{circ} )
D. ( 134^{circ} )
7
107( f l | boldsymbol{m} ) and ( boldsymbol{p} | boldsymbol{q}, ) find ( boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d} )9
108State true or false.
The sum of interior angles of a triangle
is ( 180^{circ} )
A. True
B. False
9
109All linear pairs are
A. Supplementary
B. vertically opposite
C . right angles
D. none
9
110Which of the following form the three angles of a triangle.
( boldsymbol{a})left{boldsymbol{9} boldsymbol{0}^{boldsymbol{o}}, boldsymbol{3} boldsymbol{0}^{boldsymbol{o}}, boldsymbol{5} boldsymbol{0}^{boldsymbol{o}}right} )
( b)left{40^{circ}, 40^{circ}, 100^{circ}right} )
(5)( left{50^{circ}, 60^{circ}, 70^{circ}right} )
( boldsymbol{d})left{20^{circ}, 30^{circ}, 40^{circ}right} )
A ( . d ) and ( c )
B. ( b ) and ( c )
c. ( a ) and ( c )
D. ( a ) and ( d )
9
111Lines ( mathrm{PQ} ) and ( mathrm{RS} ) intersect at ( mathrm{O} ). If
( angle P O S=2 angle S O Q, ) then the four angles
at 0 are:
A ( cdot 30^{circ}, 30^{circ}, 120^{circ}, 180^{circ} )
B . ( 60^{circ}, 60^{circ}, 120^{circ}, 120^{circ} )
c. ( 60^{circ}, 90^{circ}, 90^{circ}, 120^{circ} )
D. ( 30^{circ}, 60^{circ}, 90^{circ}, 180^{circ} )
9
112n tne Tlgure (IIVIAGE
(a) ( operatorname{Is} angle 1 )
adjacent to ( angle 2 ? )
(b) ( operatorname{ls} angle A O C )
adjacent to ( angle A O E ) ?
(c) Do ( angle C O E ) and ( angle E O D ) from linear
pair?
(d) Are ( angle B O D ) and ( angle D O A )
supplementary?
(e) is ( angle 1 ) vertically opposite to ( angle 4 ? )
(f) What is the vertically opposite angle
of ( angle 5 ? )
9
113How many pairs of vertically opposite
angles are formed?
9
114The angles of a triangle are in the ratio 2: 1: 3. Is the triangle right-angled triangle,
A. True
B. False
9
115With respect to the figure, write all
pairs of adjacent angles and all the linear pairs.
This question has multiple correct options
A. Adjacent angles: ( angle A O D & angle C O D )
B. Adjacent angles: ( angle B O C & angle C O D )
C. Linear pairs: ( angle A O D & angle B O D )
D. Linear pairs: ( angle A O C & angle B O C )
9
116n figure, ( x: y: z=5: 4: 6 . ) If ( x ) OY is a
straight line then the values of ( x, y ) and ( z )
are
This question has multiple correct options
A . ( x=60^{circ} )
В . ( y=48^{circ} )
( mathbf{c} . z=72^{circ} )
7
117Mark the correct alternative of the
following. n figure, ( A B|| C D ) and ( E F ) is a transversal intersecting ( A B ) and ( C D ) at ( P ) and ( Q )
respectively. The measure of ( angle D Q P ) is?
( A cdot 65 )
В. 25
( c .115 )
0.105
9
118Find the value of ( x )7
119n the figure, ( l | boldsymbol{m} ) and ( boldsymbol{n} | boldsymbol{p} ). If ( angle mathbf{1}=mathbf{6 0}^{circ} )
then ( angle 2=3 times angle 1 )
4 . True
3. False
9
120The pair of complementary angles from the following options are:
A . ( 30^{circ}, 150^{circ} )
В. ( 76^{circ}, 14^{circ} )
( mathbf{c} cdot 65^{circ}, 65^{circ} )
D. ( 120^{circ}, 30^{circ} )
7
121Which of the following pair of angles is
equal if ( boldsymbol{m} | boldsymbol{n} ? )
A. ( angle 1 ) and ( angle 4 )
B. ( angle 3 ) and ( angle 4 )
( c . angle 4 ) and ( angle 8 )
D. ( angle 6 ) and ( angle 8 )
9
122Find the supplementary angle of ( 40^{circ} )7
123n figure, line ( n ) is a transversal to lines ( l )
and ( m . ) Identify the following angles
alternate to ( angle d ) and ( angle g ) and angles
corresponding to angles ( angle f ) and ( angle h ) in
figure
9
124what is the measure of complementary
angle of ( 20^{circ} )
7
125In the given figure three lines ( overrightarrow{A B}, overrightarrow{C D} )
and ( widehat{E F} ) intersecting at ( 0 . ) Find the values of ( x, y ) and ( z ) it is being given
that ( boldsymbol{x}: boldsymbol{y}: boldsymbol{z}=boldsymbol{2}: boldsymbol{3}: boldsymbol{5} )
9
12657. In the given figure, AOB is a
straight line. If ZAOC=(3x-10)”,
2COD =50° and ZBOD = (x +
20)°, then ZAOC = ?
509
A
(1) 40°
(3) 80
(2) 60°
(4) 50°
7
127In the adjoining figure, name the
following pairs of angles.

Obstuse vertically opposite angles

9
128The angles are complementary and the larger is four times the smaller.7
129n figure, lines ( l_{1} ) and ( l_{2} ) intersect at ( O )
forming angles as shown in the figure. I
( x=45^{circ}, ) find the values of ( y, z ) and ( u )
9
130An angle is two-thirds of its
supplementary angle. Find the angle.
7
131( ln Delta A B C, ) if ( angle A+angle B=90^{circ}, cot B= )
( frac{3}{4}, ) then the value of ( tan A ) is :
A ( cdot frac{4}{5} )
в. ( frac{3}{4} )
( c cdot frac{4}{3} )
D. ( frac{3}{5} )
9
132If two angles are complementary of each other, then each angle is:
A. an obtuse angle
B. a right angle
c. an acute angle
D. a supplementary angle
7
133Compute the value of ( x ) in each of the
following figures
9
134( ln Delta A B C, angle C=90^{circ}, ) then the value of
( cos ^{2} A+cos ^{2} B ) is :
( mathbf{A} cdot mathbf{1} )
B. 0
( c cdot frac{1}{2} )
D. ( frac{sqrt{3}}{2} )
9
13570. What will be the value of interior
angle (in degrees and in radians)
of a pentagon with equal sides?
(1) 135° or
(2) 108° (or
(3) 90° (or T)
(4) 120º (or
9
136Find the value of unknown ( x ) in the
following diagram.
9
137In the figure, ( angle boldsymbol{E} boldsymbol{F B}=mathbf{6 6}^{circ}, angle boldsymbol{B F O}= )
( 43^{circ}, angle O G F=23^{circ}, angle O G D=y . ) Find
the value of ( y )
7
138Two complementary angles are in the ratio ( 4: 5 . ) Find the angles.9
139Calculate x. (Similar arrow markings
show parallel lines).
( A cdot 102 )
3.56
( c_{1}+a_{4} )
( D )
7
140( X ) is any point inside a ( triangle D E F ) and is joined to all vertices. From point ( boldsymbol{P} ) on ( D X, P Q | D E ) is drawn which meets ( boldsymbol{E} boldsymbol{X} ) at ( boldsymbol{Q} ) and from ( boldsymbol{Q}, boldsymbol{Q} boldsymbol{R} | boldsymbol{E} boldsymbol{F} ) is drawn
which meets ( X F ) at ( R ) Prove that
( boldsymbol{P R} | boldsymbol{D} boldsymbol{F} )
7
141In the adjacent figure ( mathrm{PQ} ) and ( mathrm{RS} ) are two
mirrors placed parallel to each other. An incident ray ( overrightarrow{A B} ) strikes the mirror ( mathrm{PQ} ) at
B, the reflected ray moves along the path ( overrightarrow{B C} ) and strikes the mirror RS at ( C )
and again reflected back along ( overrightarrow{C D} ) Prove that AB II CD.
9
142Can two acute angles form a linear
pair?
9
143Ray ( P Q ) and ray ( P R ) are perpendicular to each other. Points ( B ) and ( A ) are in the
interior and exterior of ( angle Q P R )
respectively. Ray ( P B ) and ray ( P A ) are
perpendicular to each other. Draw a figure all this rays and write-A pair of complementary angles A pair of supplementary anglesA pair of congruent angles.
9
144( overrightarrow{D C} perp overline{A B}, ) then ( angle C D B ) is equal to:
A ( .180^{circ} )
B . ( 45^{circ} )
( c cdot 90 )
D. 120
9
145An angle is equal to one-third of its supplement. Find its measure.
1.
Sol.
7
146In figure, write all pairs of adjacent
angles and all the linear pairs.
9
147an angle is ( 28^{circ} ) less than its
complement, find its measure.
7
148Measure of one angle of linear pair is given. Find the measure of another
angle:
( mathbf{5 0}^{circ} )
9
149State true or false:
If two parallel lines are intersected by a transversal, then the interior angles on
the same side of the transversal are
supplementary
A. True
B. False
7
150In the figure above, three lines intersect
at a point.
If ( boldsymbol{f}=mathbf{8 5}^{boldsymbol{o}} ) and ( boldsymbol{c}=mathbf{2 5}^{boldsymbol{o}}, ) what is the
value of ( a ? )
Note : Figure not drawn to scale
A ( cdot 60^{circ} )
B. ( 65^{circ} )
( c cdot 70^{circ} )
D. ( 75^{circ} )
9
151In the figure given, ( A B ) is a mirror, ( P Q ) is
the incident ray and ( Q R ), the reflected
ray. If ( angle mathrm{PQR}=112^{circ}, ) find ( angle mathrm{PQA} )
7
152If the complement of an angle is ( 27^{circ} )
then find its supplement.
7
153An exterior angle of a triangle is equal to the sum of two ( _{text {一一一一一一 }} ) opposite angles.
A. interior
B. exterior
c. vertical
D. none of these
9
154Given : AB || CD.
If ( angle 4 ) is an obtuse angle, then ( angle 5 ) is
A . Acute
B. Right
c. obtuse
D. Straight
9
155Find the measure of an angle which measures same as its complement7
156Find the complement of the following angle.
( 45^{circ} )
7
157Find the value of ( x ) in the following
figure.
9
158In a right angled triangle, if one of the
other two angles is ( 35^{circ} ), find the
remaining angle.
9
159In the figure, if lines ( P Q ) and ( R S )
intersect at point ( T, ) such that
( angle P R T=40^{circ}, angle R P T=95^{circ} ) and
( angle T S Q=75^{circ}, ) find ( angle S Q T )
9
160Calculate the value of ( boldsymbol{x} )7
161( P ) is any point inside the triangle ( A B C )
Hence ( angle B P C>angle B A C )
A. True
B. False
c. Ambiguous
D. Data insufficient
9
162n figure, find the values of ( x, y ) and ( z )9
163Two lines intersecting each other, prove that vertically opposite angles are equal.9
164Find the angles in each of the following:
The angles are complementary and the
smaller is ( 40^{circ} ) less than the larger.
7
165In the given figure, line ( l | ) line ( m ), line
is a transversal. Write one pair of
corresponding angles and one pair of alternate interior angles.
9
166The complement of ( left(90^{circ}-aright) ) is :
A . –
B. ( left(90^{circ}+aright) )
C. ( left(90^{circ}-aright) )
D.
7
167In the given Figure, ( A B C ) is a straight
line what is the value of ( z ? )
( mathbf{A} cdot 112^{circ} )
B. ( 92^{circ} )
c. ( 132^{circ} )
D. ( 106^{circ} )
9
168Write the measure of supplementary angle of the given angles:
( mathbf{6 0}^{circ} )
7
169Find the value of ( x ? )9
170The larger of two supplementary angles exceeds the smaller by 18 degrees. Find
them.
7
171If the angle ( x ) and ( y ) are equal, then find
the value of ( x ) and ( y )
( mathbf{A} cdot x=y=55^{circ} )
( mathbf{B} cdot x=y=45^{circ} )
( mathbf{C} cdot x=y=60^{circ} )
D ( . x=y=90^{circ} )
7
172If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
A. an isosceles triangle
B. an obtuse triangle
c. an equilateral triangle
D. a right triangle
9
173An angle is ( 45^{circ} ) less than two times of
its supplement, then the greater angle is
A ( .75^{circ} )
B . ( 100^{circ} )
( c cdot 120^{circ} )
D. ( 105^{circ} )
7
174Find the value of ( x, y ) and ( z ) in the figure.
( mathbf{A} cdot x=60^{circ}, y=120^{circ}, z=60^{circ} )
B ( cdot x=60^{circ}, y=60^{circ}, z=120^{circ} )
( mathbf{C} cdot x=120^{circ}, y=60^{circ}, z=60^{circ} )
D ( cdot x=70^{circ}, y=100^{circ}, z=70^{circ} )
9
175n figure, sides QP and RQ of ( Delta P Q R ) are
produced to points ( mathrm{S} ) and ( mathrm{T} ) respectively
If ( angle S P R=135^{circ} ) and ( angle P Q T=110^{circ} )
find ( angle P R Q )
4.85
3.65
( c cdot 45 )
0.35
9
176Based on the given figure, which of the
following statements is true?
A. ( angle 5 ) and ( angle 7 ) are supplementary angles.
B ( . angle 7=55^{circ} )
C. ( angle 8 ) and ( angle 1 ) are corresponding angles.
D. ( angle 4 ) and ( angle 5 ) are alternate angles.
9
177n the figure ( angle B A C=75^{circ}, angle A B C= )
( 35^{circ} . ) Find the measures of ( angle B A Z )
9
178Show that if a straight line is perpendicular to one of the two or more parallel lines, then it is also perpendicular to the remaining lines.7
179A bicycle wheel makes four and half turns, then the number of right angles through which it turns is
A . 16
B. 18
c. 20
D. 8
9
180One of the angles forming a linear pair is a right angle. What can you say about its other angle?9
181n the given figure if ( A B | D E, angle B A C= )
( 35^{circ} ) and ( angle C D E=53^{circ}, ) find ( angle D C E )
9
182If two straight lines intersect the measures of the vertically opposite angles are
A. equal
B. not equal
c. cannot be determined
D. none of these
9
183find the value of ( x ) in each of the
following figures.
(a)
9
184n figure, line ( n ) is a transversal to lines
and ( m ). Identify the following pairs of
interior and exterior angles on the same
side of the transversal in figure.
9
185What do you mean by linear pair of angles?9
186Mark the correct alternative of the
following.
In figure, if ( A O B ) and ( C O D ) are straight
lines. Then, ( boldsymbol{x}+boldsymbol{y}=? )
A .120
B. 140
( c .100 )
D. 160
9
187In figure, name each linear pair and
each pair of vertically opposite angles
9
188Find ( x )9
189If two parallel lines are cut by a transversal, then each pair of
corresponding angle are
A . congruent
B. obtuse
c. acute
D. ( 90^{circ} )
9
190In the figure above, point ( mathrm{B} ) lies on ( overline{boldsymbol{A} C} ).
Find a possible value of ( boldsymbol{X}, ) if ( boldsymbol{X} ) and ( boldsymbol{Y} )
are integers.
A ( .30^{circ} )
B. ( 35^{circ} )
( c cdot 40^{circ} )
( D .50 )
E. 55
7
191In a ( Delta A B C, D, E ) and ( F ) are respectively, the mid-points of BC, and
AB. If the lengths of side ( A B, B C ) and ( C A ) ( operatorname{are} 7 mathrm{cm}, 8 mathrm{cm}, ) and ( 9 mathrm{cm}, ) respectively
find the perimeter of ( Delta D E F )
9
192What is the measure of complementary
angle of ( 32^{circ} ? )
A ( cdot 48^{circ} )
B. 78
( c cdot 58 )
( D cdot 68 )
7
193Find the values of the unknown ( x ) and
n the following diagram.
9
194( A B | C D ) and ( A C M ) is a straight line
( angle B A C ) is equal to:
A ( cdot 106^{circ} )
B. ( 108^{circ} )
( mathrm{c} cdot 110^{circ} )
D. ( 109^{circ} )
9
195( square A B C D ) is a trapezium in which
( boldsymbol{A B} | boldsymbol{D C} ) and ( angle boldsymbol{A}=angle boldsymbol{B}=mathbf{4 5}^{boldsymbol{o}} . ) Find ( angle boldsymbol{C} )
and ( angle D ) of the trapezium.
A ( cdot 135^{circ} ) each
B . ( 125^{circ}, 145^{circ} )
c. ( 145^{circ}, 125^{circ} )
D . ( 115^{circ}, 155^{circ} )
9
196Write all pairs of vertically opposite
angles.
9
197n fig, if ( boldsymbol{A B}|boldsymbol{C D}, boldsymbol{C D}| boldsymbol{E F} ) and ( boldsymbol{y} )
( z=3: 7 ) find ( x )
7
198If two straight lines intersect, the measures of the vertically opposite angles are
A. equal
B. not equal
c. cannot be determined
D. Nont of these
9
199Read the following statements which are taken as axioms:
(i) If a transversal intersects two
parallel lines, then corresponding angles are not necessarily equal.
(ii) If a transversal intersect two parallel lines, then alternate interior angles are
equal

Is this system of axioms consistent?

7
200If true then enter 1 and if false then
enter 0
Can two obtuse angles be
supplementary?
7
201Find the value of unknown ( x ) in the
following diagram.
9
202In the figure given ( L_{1} ) and ( L_{2} ) are
parallel. The sum of the angles ( boldsymbol{alpha}, boldsymbol{beta}, boldsymbol{gamma} )
marked in the diagram is:
( A cdot 180^{circ} )
В. ( 270^{circ} )
( c cdot 360^{circ} )
D. ( leq 270^{circ} )
9
203n the figure if ( B D | E F ), then ( angle C E F ) is
A ( cdot 100^{circ} )
В. 120
( c cdot 140^{circ} )
( 0.160^{circ} )
7
204State true or false:
Angles forming a linear pair are supplementary.
A. True
B. False
7
205Find the measure of the supplementary
angle of ( 132^{circ} )
A ( cdot 48^{circ} )
B. ( 32^{circ} )
( c cdot 42^{circ} )
( D cdot 38^{circ} )
7
206Mark the correct alternative of the
following. If the measures of the angles of a
triangle are ( (2 x)^{o},(3 x-5)^{o} ) and ( (4 x- )
13) ( ^{circ} . ) Then the value of ( x ) is?
A . 22
B . 18
c. 20
D. 30
9
207in the given figure sides of the angles
are parallel. Find ( boldsymbol{x} ) and ( boldsymbol{y} ) if ( angle boldsymbol{A}=mathbf{5 5}^{circ} )
9
208The difference between the supplement
of an angle and the angle is ( 36^{circ} . ) The
supplement is:
A .72
B. ( 108^{circ} )
( c cdot 63 )
D. 27
7
209Find the ( x ) and ( y ) in the following figure:9
210If ( X ) is a point on the line ( A B . Y ) and ( Z )
are points outside such that ( angle A X Y= )
( 45^{circ} ) and ( angle Y X Z=150^{circ}, ) then ( angle A X Z ) is
equal to:
A ( cdot 120^{circ} )
B. ( 135^{circ} )
( c cdot 150^{circ} )
D. ( 165^{circ} )
7
211If true then enter 1 and if false then
enter 0

Can an acute angle be adjacent to an obtuse angle?

9
212In the figure, find ( x )7
213As shown in above figure which of the
following angles are equal
A ( . angle 1 ) and ( angle 2 )
B. ( angle 1 ) and ( angle 3 )
( c cdot angle 1 ) and ( angle 4 )
D. None of the above
7
214Observe the angles shown in the figure
and write the following pair of angles.
(1) Interior alternate angles
(2) Corresponding angles
(3) Interior angles
7
215In the figure, if linel ( | ) m. What is the
value of ( x )
7
216Lines ( P Q ) and ( R S ) intersect at ( O ). If
( angle P O S=2 angle S O Q ) then the four angles
at ( boldsymbol{O} ) are
В. ( 60^{circ}, 60^{circ}, 120^{circ}, 120^{circ} )
c. ( 60^{circ}, 90^{circ}, 90^{circ}, 120^{circ} )
D. ( 30^{circ}, 60^{circ}, 90^{circ}, 180^{circ} )
9
217The angle between the internal and the
external bisectors of an angle of a triangle is
A ( .90^{circ} )
B. ( 180^{circ} )
( c cdot 270^{circ} )
D. ( 30^{circ} )
9
218In fig. find the values of ( x ) and ( y ) and ( t )
Show that ( boldsymbol{A B} | boldsymbol{C D} )
A. ( x=100 ) and ( y=130 )
B . ( x=230 ) and ( y=130 )
c. ( x=130 ) and ( y=130 )
D. None of these
9
219The measure of an angle is three times the measure of its complement. The angles are:
A ( cdot 20^{circ}, 60^{circ} )
B. ( 30^{circ}, 60^{circ} )
c. ( 45^{circ}, 135^{circ} )
D . 22.5^, 67.5 ( ^{circ} )
7
220In the given figure, ( a ) is greater than ( b ) by
two third of a right angle. The values of
( a ) and ( b ) are
A ( cdot 100^{circ}, 80^{circ} )
B . ( 105^{circ}, 75^{circ} )
( mathbf{c} cdot 90^{circ}, 90^{circ} )
D. ( 120^{circ}, 60^{circ} )
7
221In the figure, if ( angle q=140 ), what is the
value of ( angle boldsymbol{r}-angle boldsymbol{p} ? )
( A cdot 0^{circ} )
B. ( 10^{circ} )
( c .90^{circ} )
D. 130
9
222In the given figure, the straight line ( A B )
and ( mathrm{CD} ) are parallel to each other. If
angle ( boldsymbol{p}=mathbf{5 5}^{circ}, ) and, ( boldsymbol{q}=mathbf{4 3}^{boldsymbol{o}} ) then
answer the given questions. Find the
value ( x )
( mathbf{A} cdot 55^{circ} )
B. ( 82^{circ} )
( mathbf{c} cdot 98^{circ} )
D. ( 108^{circ} )
7
223In the given figure ( A B | C D ). find the
value of ( x ) and ( y )
A ( cdot x=35^{circ}, y=65^{circ} )
B . ( x=95^{circ}, y=65^{circ} )
C . ( x=85^{circ}, y=65^{circ} )
D. ( x=25^{circ}, y=65 )
7
224In fig name all the pairs of adjacent angles.9
225Choose the pair of complementary angles.
A ( cdot 30^{circ}, 150^{circ} )
B. ( 76^{circ}, 14^{circ} )
( mathbf{c} cdot 65^{circ}, 65^{circ} )
D. ( 120^{circ}, 30^{circ} )
7
226If true then enter 1 and if false then
enter 0
Can two adjacent angles be
complementary?
7
227If ( l | boldsymbol{m} ) and ( mathrm{CD} ) is transversal, ( angle mathbf{1} ) and ( angle mathbf{2} )
represents
A. Co-interior angles
B. Corresponding angles
c. Alternate interior angles
D. Exterior angles
9
228Measure of one angle of linear pair is
( 108^{circ}, ) then find the measure of another angle.
9
229Find the value of the unknown interior
angle ( x ) in the following figure.
9
230In the adjoining figure, identify the pair of corresponding angles9
231Two supplementary angles differ by ( 22^{0} )
Find the angles.
9
232( A B ) is a straight line and ( O ) is a pont
lying on ( A B . A ) line ( O C ) is drawn from ( O )
such that ( angle C O A=36^{circ} . O D ) is a line
within ( angle C O A ) such that ( angle D O A=frac{1}{3} ) ( angle C O A ). If ( O E ) is a line within the ( angle B O C )
( angle B O E=frac{1}{4} angle B O C, ) then ( angle D O E ) must
be:
A ( cdot 60^{circ} )
В ( cdot 132^{circ} )
( c cdot 144^{circ} )
D. ( 108^{circ} )
9
233fray ( O S ) stand on a line ( P O Q ). Ray ( O R )
and ray ( boldsymbol{O} boldsymbol{T} ) are angle bisectors of
( angle P O S ) and ( angle S O Q ) respectively. If
( angle P O S=x, ) find ( angle R O T )
7
234Find the measure of the complementary
angle of ( 90^{circ} )
A ( cdot 0^{circ} )
B . 45
( c .90 )
D. 60
7
235One angle of linear pair is a right angle, then find the measure of another angle.9
236Which of the following statements are true (T) and which are false (F) :

Sum of the three angles of a triangle is
( mathbf{1 8 0}^{circ} )
A. True
B. False

9
237Which of the following pairs is pair of interior formed by two parallel lines and on the same side of the transversal?
A ( cdot 30^{circ}, 60^{circ} )
( ^{0}, 66,6^{circ} )
В. ( 30^{0}, 150^{0} )
c. ( 60^{circ}, 130^{circ} )
D. ( 50^{circ}, 120^{0} )
9
238Draw an angle and label it as ( angle B A C )
Construct another angle, equal to ( angle B A C )
7
239( angle A ) and ( angle B ) are liner pair of angles. If
( 4 angle A=5 angle B . ) then find ( angle A ) and ( angle B )
9
240The angle between the lines ( x+y- )
( mathbf{3}=mathbf{0} ) and ( boldsymbol{x}-boldsymbol{y}+mathbf{3}=mathbf{0} ) is ( boldsymbol{alpha} ) and the
acute angle between the lines ( x- ) ( sqrt{3 y}+2 sqrt{3}=0 ) and ( sqrt{3 x}-y+1=0 )
is
( beta . ) Which one of the following is
correct?
A. ( alpha=beta )
в. ( alpha>beta )
c. ( alpha<beta )
D. ( alpha=2 beta )
7
241Angles ( Q ) and ( R ) of a ( Delta P Q R ) are ( 25^{circ} ) and
( 65^{circ} . ) Write which of the following is true:
1. ( boldsymbol{P Q}^{2}+boldsymbol{Q} boldsymbol{R}^{2}=boldsymbol{R} boldsymbol{P}^{2} )
2. ( boldsymbol{P Q}^{mathbf{2}}+boldsymbol{R} boldsymbol{P}^{2}=boldsymbol{Q} boldsymbol{R}^{2} )
3. ( boldsymbol{R} boldsymbol{P}^{2}+boldsymbol{Q} boldsymbol{R}^{2}=boldsymbol{P} boldsymbol{Q}^{2} )
9
242Construct the following angles using
set-squares: ( 150^{circ} )
9
243Name the pairs of adjacent angles in
the figures.
9
244An angle is such that the ratio between its complementary and supplementary angles is ( 1: 4 . ) Then the angle measure
is?
A ( cdot 45^{circ} )
B. ( 60^{circ} )
( c cdot 75^{circ} )
D. ( 90^{circ} )
7
245Find the value of ( x )9
246Can two angles be supplementary if both of them are: (i) acute (ii) obtuse
(iii) right?
7
247Find the value of ( x ) in given figure if
( boldsymbol{A B} | boldsymbol{C D} )
( x ) is the exterior angle of ( angle P Q R )
A ( .275^{circ} )
B . ( 280^{circ} )
( mathbf{c} cdot 285^{circ} )
D. ( 295^{circ} )
7
248If a straight line falling on two straight
lines makes the interior angles on the
same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is
less than two right angles?
7
249Find the measure of an angle if its supplement-three times complement
( =20^{circ} 30^{prime} 40^{prime prime} )
7
250( A B ) and ( C D ) intersects each other at
point ( O . ) Measure of one angle formed by
intersection is ( 120^{circ}, ) then the measure
of another three angles are ( 60^{circ}, 120^{circ}, 60^{circ} )
A. True
B. False
9
25113. In the given figure, find a+b+c+d.
60°
s
800
120°
7
252Manasa says, Each angle in any pair of complementary angles is a always
acute. Do you agree? Give reason.
7
253In the adjacent figure, a line ( n ) falls on
lines ( l ) and ( m ) such that the sum of the
interior angle 1 and 2 is less than ( 180^{circ} )
then what can you say about lines ( l ) and
7
254( f angle 2=(3 x-10)^{circ} ) and ( angle 8=(5 x-30)^{circ} )
find the measures of ( angle 2 ) and ( angle 8 )
This question has multiple correct options
( mathbf{A} cdot angle 2=20^{circ} )
( mathbf{B} cdot angle 8=20^{circ} )
( mathbf{c} cdot angle 2=40^{circ} )
D. ( angle 8=40^{circ} )
7
255If true then enter 1 and if false then
enter 0

Can two obtuse angles form a linear pair?

9
256If one angle of a linear pair is acute, then its other angle will be
A. obtuse angle
B. Acute angle
c. Right angle
D. None of these
9
25761. In APQR, the bisectors of 20
and ZR meet each other at point
Tand ZQPR = 80º and ZPRT =
30°, then ZOTR will be
(1) 110 (2) 120°
(3) 130° (4) 140
9
258In the given figure, ( A B | D C, angle B A D= )
( 90^{0}, angle C B D=28^{0} ) and ( angle B C E=65^{0} )
Then ( angle A B D=? )
( A cdot 32 )
B .37
( c cdot 43 )
( D cdot 53^{circ} )
9
259Find the measure of an angle, if seven
times its complement is ( 10^{circ} ) less than
three times its supplement
A .40
B . 25
( c cdot 30^{circ} )
D. 15
7
260In the adjoining figure, parallel lines are
shown with similar markings. Find ( angle x )
if ( angle x=5 angle y )
( mathbf{A} cdot 30^{circ} )
B. ( 60^{circ} )
c. ( 150^{circ} )
D. ( 170^{circ} )
7
261Two angles measure ( (30-a)^{circ} ) and
( (125+2 a)^{circ} . ) If each one is the
supplement of the other, then the value
of a is:
A . 45
B. 35
( c cdot 25 )
D. ( 65^{circ} )
7
262In the given figure, QP II ML and other
angles are shown. Find the value of ( x )
( mathbf{A} cdot 60^{circ} )
B ( .35^{circ} )
( c cdot 20^{circ} )
( D cdot 30^{circ} )
7
263In the given figure, we have ( angle 1=angle 3 )
and ( angle 2=angle 4 ), then:
4. ( angle A=angle C )
3. ( angle A=angle D )
( c cdot angle A=angle B )
begin{tabular}{l}
( . angle B=angle L ) \
hline
end{tabular}
9
264Find ( boldsymbol{x}+boldsymbol{y}+boldsymbol{z} )
A ( cdot x+y+z=180 )
в. ( x+y+z=360^{circ} )
c. ( x+y+z=480^{circ} )
D. ( x+y+z=540 )
9
265Find the measure of the angles of a
triangle in each of the following cases:
One of the acute angles of a
right triangle is ( 63^{circ} . ) Find the other angle.
9
266Find the value of ( x ) in each of the
following figures?
9
267In a triangle ( A B C, ) the angle bisectors of
angle ( A B C ) and ( A C B ) meet at point ( 0 . ) If ( angle )
( mathrm{BAC}=32^{circ}, ) find ( angle mathrm{BOC} )
9
268Measure of one angle of linear pair is given. Find the measure of another
angle:
( 111^{circ} )
9
269Find the values of the unknown ( x ) and ( y )
in the following diagram.
9
270IN the figure || and ( n ) is a ttansversal
such that ( angle 3: angle 8=1: 2 . ) Find ( angle 4 ) and
( angle 3 )
7
271Write the measure of supplementary angle of the given angles:
( mathbf{1 0 0}^{circ} )
7
272From the adjoining figure, calculate the
values of ( boldsymbol{a} )
A ( cdot 46^{circ} )
B. 38
( c cdot 56^{circ} )
D. none of the above
9
273What is the value of ( x ) in the given
figure?
( mathbf{A} cdot 71^{circ} )
B ( .90^{circ} )
( c cdot 19^{c} )
( D cdot 24^{c} )
7
274In the above sided figure,if
( Q T perp P R ., angle T Q R=40^{circ} ) and ( angle S P R= )
( 30^{circ} ),find ( x ) and ( y )
9
275If the angles of a triangle are in the ratio ( 1: 2: 7, ) then the triangle is:
A . an acute angled triangle
B. an obtuse angled triangle
c. a right angled triangle
D. a right angled isosceles triangle
9
276Identify whether the following pairs of angles are complementary or
supplementary:
( 63^{circ}, 27^{circ} )
7
277According to figure, find the values of
angles ( x, y ) and ( z )
9
278In the given figure, if ( boldsymbol{x}+boldsymbol{y}=boldsymbol{w}+boldsymbol{z} )
then prove that ( A O B ) is a line.
7
279( A B | overrightarrow{C D} ) in the following figure. ( overline{X Y} ) is
the transversal. If ( m angle P Q A=140^{circ}, ) find
the measure of remaining angles:
9
280( a, b, c ) are three adjacent angles at a
point ( O ) on a line ( A B ) such that their
degree measures are three consecutive
numbers. Find values of ( a, b, c )
7
281For an angle ( x^{2} ), find:
The supplementary angle.
7
282In the given figure, which line is
perpendicular to AB?
A. CD
B. EF
( c cdot G H )
( D cdot mid J )
9
283What are complementary and supplementary angles?7
284Draw diagrams illustrating each of the following situation:
(a) Three straight lines which do not pass through a fixed point.
(b) A point and rays emanating from that point such that the angle between any two adjacent rays is an acute angle.
(c) Two angles which are not adjacent angles, but still supplementary.
(d) Three points in the plane which are equidistant from each other
7
285Find the complement of the angles
represented in given figure.
7
286n Fig., if ( boldsymbol{A B} | boldsymbol{C D} ) and ( boldsymbol{C D} | boldsymbol{E} boldsymbol{F} ), find
( angle A C E )
7
287Find the complementary angle of ( 45 frac{1}{2}^{circ} )7
288Mark the correct alternative of the
following.

If the measures of the angles of a triangle are ( (2 x-5)^{o},left(3 x-frac{1}{2}right) ) and ( left(30-frac{x}{2}right), ) then ( x=? )
A ( cdot frac{311}{9} )
в. ( frac{309}{11} )
c. ( frac{310}{9} )
D. ( frac{301}{9} )

9
289n Fig, POQ is a line. The value of ( x ) is:
A . ( 20^{circ} )
B ( cdot 25^{circ} )
( c cdot 30^{0} )
D. 35
7
290By simply looking at the pair of angles
given in figure. State which of the angle
in the pairs is greater.
9
291If ( l | boldsymbol{m} ) and ( boldsymbol{m} | boldsymbol{n} ) then:
A . ( l | )
в. ( l | )
c. ( m | ) n
D. ( l | n )
7
292Lines ( mathrm{PQ} ) and RS intersect at ( 0 . ) If ( angle P O R )
is three times ( angle R O Q, ) then ( angle S O Q ) is
A ( cdot 120^{circ} )
B. 150
( c cdot 135 )
D. 45
9
293Fill up the table on finding complementary angle of given angle:
( begin{array}{ll}text { Angle }-1 & text { Angle }-2 \ text { 500 }end{array} )
(1)
( 50^{circ} ) 1

(2) , a ( – ) ( – ) ( 63^{circ} )
(3) an ( 47^{circ} ) and ( – ) (4) (i)
(5)
(6) ” begin{tabular}{ll}
( 47^{circ} ) & ( – ) \
( 56^{circ} ) & ( 12^{circ} ) \
hline & \
( 67^{circ} ) & \
hline
end{tabular} “of
7
294The sum of all six exterior angles of triangle is
A . 180
в. 360
c. 720
D. 90
9
295In the given figure, ( angle A O B=90^{circ} ) and
( C O D ) is a straight line. The values of ( x )
and ( y ) are respectively.
A ( cdot 25^{circ} ) and ( 15^{circ} )
B ( cdot 20^{circ} ) and ( 30^{circ} )
( mathbf{c} cdot 15^{circ} ) and ( 45^{circ} )
D. ( 10^{circ} ) and ( 60^{circ} )
9
296Find the value of ( x ) in each of the
following figure, if ( boldsymbol{I} | boldsymbol{m} )
7
297Find the value of ( x ) in each of the
following figure :
9
298O is any point inside a triangle ABC. The bisector of ( angle A O B, angle B O C ) and ( angle C O A )
meet the sides, ( A B, B C ) and ( C A ) in point D, E and F respectively, therefore,
( A D times B E=D B times F A )
A. True
B. False
9
299Find the measure of the supplementary
angle pair of ( 60^{circ} . ) (in degrees)
7
300n fig, then ( angle A+angle B+angle C+angle D+ )
( angle boldsymbol{E}+angle boldsymbol{F}= )
A ( cdot 180^{circ} )
B. ( 270^{circ} )
( c .360^{circ} )
D. ( 540^{circ} )
9
301n figure if ( x=y ) and ( a=b, ) then prove
that ( r | n )
7
302Complement angle of
A . ( 77.4^{circ} )
B .67 .3
( c cdot 76.3^{circ} )
D. ( 77.3^{circ} )
7
303The supplement angle of the
complement of ( 30^{circ} ) is
A ( .150^{circ} )
B . ( 120^{circ} )
( mathrm{c} cdot 90^{circ} )
D. ( 210^{circ} )
7
304In the adjoin figure, ( A B C ) is an isocules triangle with ( A B=A C & L M ) is
parallel to ( B C . ) If ( angle A=50^{circ}, ) find ( angle L M C )
9
305Find the value of ( x ) and ( y )
A ( cdot 60^{circ}, 45^{circ} )
B ( .45^{circ}, 60^{circ} )
( mathbf{c} cdot 45^{circ}, 45 )
D. ( 60^{circ}, 60^{circ} )
7
306Measure of one angle of linear pair is given. Find the measure of another
angle:
( mathbf{2 0}^{circ} )
9
307Three times the complement of an angle
is ( 20^{circ} ) more than its supplement. Find
the angle.
7
308If true then enter 1 and if false then
enter 0
Can two obtuse angles be complement
to each other?
7
309Find the measure of the alternate angle
of the angle of measure of ( 65^{0} )
A ( cdot 65^{circ} )
B . 25
( mathrm{c} cdot 115^{circ} )
D. Depends on the orientation of lines
9
310Write down each pair of adjacent angles
shown in figure.
9
311OA and OB are opposite rays.
f ( x=75^{circ}, ) what is the value of ( y ? )
( A cdot 105^{circ} )
B ( .75^{circ} )
( mathbf{c} cdot 45^{circ} )
D ( .15^{circ} )
9
3121.
An angle is equal to one-third of its supplement. Find its measure.
7
313If a transversal intersects a pair of lines
in such a way that a pair of alternate angles are equal, then the lines are
A. parallel
B. perpendicular
c. transversal
D. none of these
9
314Using information given in the adjacent
figure, find the values of ( x ) and ( y )
9
315Let lines ( A B ) and ( C D ) intersect at ( O )
If ( angle A O C+angle B O E=70^{circ} ) and
( angle B O D=40^{circ}, ) find ( angle B O E )
7
316Mark the correct alternative of the
following.
In figure, ( A B|| C D ) and ( E F ) is a transversal
intersecting ( A B ) and ( C D ) at ( P ) and ( Q )
respectively. The measure of ( angle D P Q ) is
( mathbf{A} cdot 100^{circ} )
B . ( 80^{circ} )
( mathbf{c} cdot 110^{circ} )
D. ( 70^{circ} )
7
317( boldsymbol{P Q} | boldsymbol{R} boldsymbol{S}, ) find the measure of ( boldsymbol{m} )
กก
90
137
9
318Twp angles form a linear pair. If one of these is one-fourth of the other, find the positive difference between the two
angles.( in degrees )
9
319If the difference of two supplementary
angles is ( 40^{0}, ) then the measurement of
the greater angle is:
A ( cdot 65^{circ} )
B . ( 110^{circ} )
( c cdot 130^{circ} )
D. 220
7
320From the given figure, we can find that
( angle A B C=47^{circ} )
A. True
B. False
9
321( triangle P Q R ) is an isosceles triangle with
( P Q=P R, Q P ) is produced to ( S ) and ( P T )
bisects the extension angle ( 2 x^{circ} . ) Prove
that ( angle Q=x^{o} ) and hence prove that
( boldsymbol{P T} | boldsymbol{Q} boldsymbol{R} )
9
322If the straight lines ( A B ) and ( X Y ) intersect at the point 0 and ( angle A O X=3 angle X O B )
then the four angles formed at 0 are:
A ( cdot 30^{circ}, 30^{circ}, 90^{circ}, 210^{circ} )
В. ( 30^{circ}, 30^{circ}, 150^{circ}, 150^{circ} )
c. ( 45^{circ}, 135^{circ}, 90^{circ}, 90^{circ} )
D . ( 45^{circ}, 45^{circ}, 135^{circ}, 135^{circ} )
9
323Lines ( m ) and ( n ) are cut by a transversal
so that ( angle 1 ) and ( angle 5 ) are corresponding
angles. If ( angle mathbf{1}=mathbf{2 6} boldsymbol{x}-mathbf{7}^{o} ) and ( angle mathbf{5}= )
( 20 x+17^{circ} . ) What value of ( x ) makes the
lines ( m ) and ( n ) parallel?
A . 5
B. 4
c. ( _{4} frac{1}{2} )
D. ( _{3} frac{1}{4} )
7
324In the adjoining figure, name the
following pairs of angles.
Equal supplementary angles
7
325In the given diagram CE is parallel to
AD and the measures of two angles at ( mathrm{B} )
and ( C ) have been indicated.Then ( angle D A B )
is equal to
( A cdot 30 )
B. 35
( c cdot 40 )
D. cannot be determined
9
326n fig. I I I and p I Find values of ( x, y )
( z, t )
9
327Measure of one angle of linear pair is given. Find the measure of another
angle:
( mathbf{1 0 7}^{circ} )
9
328In the given figure, ( A B=B C ) and
( A C=C D . ) Prove that: ( angle B A D )
( angle A D B=3: 1 )
9
329Find the value of unknown ( x ) in the
following diagram
9
330In each of the following figure ( A B | C D ) Find the value of ( x ) in each case7
331n the figure measure of two angles are
given. If line ED ( | operatorname{seg} A B ) and ( E-C-D ) then
find the values of ( x ) in degrees.
( A cdot 35 )
B. ( 55^{circ} )
( c cdot 65^{circ} )
( D .95 )
9

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