Lines And Angles Questions

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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.

Lines And Angles Questions

List of lines and angles Questions

Question No Questions Class
1 n 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
2 In 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
3 Find 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
4 Find the supplement of the following
angle
( mathbf{1 2 0}^{circ} )		 7
5 State 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
6 Show that difference of any two sides of
a triangle is less than to the third side.		 9
7 An 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
8 If ( A, B ) are complementary angles, then ( cos ^{2} A+cos ^{2} B ) 7
9 Find the angle which is supplementary of itself 7
10 In the given figure, ( p | q ) and ( r | s . ) Find
the values of ( x, y ) and ( z )		 7
11 Find the angle which is ( 56^{circ} ) more than
its complement
A . 73
B. 83
c. 45
D. 68		 7
12 If 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
13 Fill 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
14 In 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
15 If 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
16 If ( 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
17 In 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
18 The 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
19 Which 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
20 In 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
21 53. In a A ABC, if ZA = 120° and
AB = AC, then ZB is equal to
(1) 35° (2) 60°
(3) 30° (4) 80° 		9
22 State 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
23 The 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
24 Measure 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
25 In 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
26 Calculate 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
27 Mark 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
28 In. 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
29 Find the values of the unknown ( x ) and ( y )
in the following diagram		 9
30 If 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
31 In the adjoining figure, identify the pair of alternate interior angles. 9
32 Find ( frac{boldsymbol{x}+boldsymbol{u}+boldsymbol{y}+boldsymbol{z}}{mathbf{5 0}} ) 9
33 n ( 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
34 In figure, write down each pair of
vertically opposite angles		 9
35 If two intersecting lines are intersected by a transversal, then corresponding angles are equal.
A. True
B. False
c. Ambiguous
D. Data Insufficient		 7
36 n figure, OA and OB are opposite rays if
( x=25^{circ}, ) what is the value of ( y ? )		 9
37 If 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
38 In a right triangle the two acute angles are in the ratio ( 7: 11 . ) Find the measure
of acute angles.		 9
39 f ( 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
40 Indicate which pairs of angles are:
Vertically opposite angles.
( A cdot 184 )
( B cdot 2 & 4 )
( c cdot 1 & 3 )
( D cdot 5 & 4 )		 9
41 In the below figure ( A B, C D ) and ( E F ) are
three lines concurrent at ( O ). Find the
value of ( y )		 7
42 In given figure find ( x )
( mathbf{A} cdot 110^{0} )
( mathbf{B} cdot 120^{0} )
( mathbf{c} cdot 130^{circ} )
D. ( 140^{circ} )		 9
43 Find 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
44 Two 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
45 61. The angle in a semi-circle is
(1) a reflex angle
(2) an obtuse angle
(3) an acute angle
(4) a right angle 		7
46 What is the value of ( a-b )
A ( cdot 180^{circ} )
B ( .60^{circ} )
( c cdot 70^{circ} )
( D cdot 120 )		 9
47 Angles forming a linear pair can both be acute angles.
A. True
B. False
c. Ambiguous
D. Data Insufficient		 9
48 Define adjacent angle. 9
49 Find ( x, y, z ) 9
50 In 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
51 In 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
52 Write all pairs of angles of linear pair. 9
53 Write the complement (in degree) of
each of the following angles: ( 30^{circ} )		 7
54 Find the value of unknown ( x ) in the
following diagram.		 9
55 Find the complementary of the angle
( mathbf{3 0}^{circ} )		 7
56 Find the value of the unknown interior
angle ( x ) in the following figure.		 9
57 Consider 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
58 Two 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
59 The 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
60 In 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
61 State True or False
From the following figure, we can say:
( angle A C D=angle C B E )
( 4 . ) True
3. Falss		 9
62 In 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
63 n given figure the value of ( x ) is :
( mathbf{A} cdot 120^{circ} )
B. ( 110^{circ} )
( c cdot 80^{c} )
D. ( 100^{circ} )		 9
64 In 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
65 How many pair of vertically opposite
angles are formed?		 9
66 Find the value of ( x ) 9
67 From 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
68 Find 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
69 If two supplementary angles have equal measure, what is the measure of each
angle?		 7
70 Two adjacent angles whose sum is ( 180^{circ} ) is called
A. complementary angles
B. linear pair
c. vertically opposite angles
D. none		 9
71 Identify the following pairs of angles are complementary or supplementary:
( 80^{circ}, 10^{circ} )		 7
72 If two parallel lines are intersected by a transversal, then prove that bisectors of the interior angles from a rectangle. 9
73 14. Find the measure of an angle if seven times its complement
is 10° less than three times its supplement. 		7
74 If one angle of a triangle is ( frac{pi}{4} ) and other
angle is ( 90^{circ} ) then find the third angle in
degree measure.		 7
75 n 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
76 In 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
77 In 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
78 From the following figure, can we say
that ( boldsymbol{A B}>boldsymbol{C D} )
If true then enter 1 else enter 0 .		 9
79 Find the angles in a straight line 9
80 A 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
81 Find 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
83 In the figure ( l / / m ) and ( p ) is a
transversal, find the value of ( x, ) giving
necessary reasons.		 9
84 In figure,prove AB ( | mathrm{EF} ) 7
85 In figure, ( A, B, C ) are collinear points.
Name two linear pairs.		 9
86 Prove that the sum of angles of a
triangle is 180		 9
87 Find ( x ) in the following figure ( (A B | C D) ) 9
88 In 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
90 Find the values of the unknown ( x ) and ( y )
in the following diagram		 9
91 Find the complementary angle of ( 60^{circ} ) 7
92 Find the complement of each of the
following angles:		 7
93 Two complementary angles differ by ( 10^{circ} ) Find the angles 7
94 In 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
95 By simply looking at the pair of angles
given in figure. State which of the angle in the pairs is greater.		 9
96 Write the supplement of each of the
following angles: ( 138^{circ} )		 7
97 Find the angle, if its complement is one-
fourth of its supplement.		 7
98 p 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
99 n 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
100 If true then enter 1 and if false then
enter 0

Can two acute angles form a linear pair?

 9
101 In 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
102 n fig. ( 1, ) AOB is a straight line, the value
of ( x ) is :
( A cdot 60 )
B. 30
( c cdot 20 )
( D )		 7
103 n 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
104 Find ( x ) in the following figures: 9
105 The 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
106 Find 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
108 State true or false.
The sum of interior angles of a triangle
is ( 180^{circ} )
A. True
B. False		 9
109 All linear pairs are
A. Supplementary
B. vertically opposite
C . right angles
D. none		 9
110 Which 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
111 Lines ( 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
112 n 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
113 How many pairs of vertically opposite
angles are formed?		 9
114 The angles of a triangle are in the ratio 2: 1: 3. Is the triangle right-angled triangle,
A. True
B. False		 9
115 With 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
116 n 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
117 Mark 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
118 Find the value of ( x ) 7
119 n 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
120 The 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
121 Which 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
122 Find the supplementary angle of ( 40^{circ} ) 7
123 n 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
124 what is the measure of complementary
angle of ( 20^{circ} )		 7
125 In 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
126 57. 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
127 In the adjoining figure, name the
following pairs of angles.

Obstuse vertically opposite angles

 9
128 The angles are complementary and the larger is four times the smaller. 7
129 n 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
130 An 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
132 If 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
133 Compute 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
135 70. 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
136 Find the value of unknown ( x ) in the
following diagram.		 9
137 In 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
138 Two complementary angles are in the ratio ( 4: 5 . ) Find the angles. 9
139 Calculate 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
141 In 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
142 Can two acute angles form a linear
pair?		 9
143 Ray ( 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
145 An angle is equal to one-third of its supplement. Find its measure.
1.
Sol. 		7
146 In figure, write all pairs of adjacent
angles and all the linear pairs.		 9
147 an angle is ( 28^{circ} ) less than its
complement, find its measure.		 7
148 Measure of one angle of linear pair is given. Find the measure of another
angle:
( mathbf{5 0}^{circ} )		 9
149 State 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
150 In 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
151 In 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
152 If the complement of an angle is ( 27^{circ} )
then find its supplement.		 7
153 An 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
154 Given : AB || CD.
If ( angle 4 ) is an obtuse angle, then ( angle 5 ) is
A . Acute
B. Right
c. obtuse
D. Straight		 9
155 Find the measure of an angle which measures same as its complement 7
156 Find the complement of the following angle.
( 45^{circ} )		 7
157 Find the value of ( x ) in the following
figure.		 9
158 In a right angled triangle, if one of the
other two angles is ( 35^{circ} ), find the
remaining angle.		 9
159 In 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
160 Calculate 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
162 n figure, find the values of ( x, y ) and ( z ) 9
163 Two lines intersecting each other, prove that vertically opposite angles are equal. 9
164 Find the angles in each of the following:
The angles are complementary and the
smaller is ( 40^{circ} ) less than the larger.		 7
165 In 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
166 The complement of ( left(90^{circ}-aright) ) is :
A . –
B. ( left(90^{circ}+aright) )
C. ( left(90^{circ}-aright) )
D.		 7
167 In 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
168 Write the measure of supplementary angle of the given angles:
( mathbf{6 0}^{circ} )		 7
169 Find the value of ( x ? ) 9
170 The larger of two supplementary angles exceeds the smaller by 18 degrees. Find
them.		 7
171 If 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
172 If 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
173 An 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
174 Find 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
175 n 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
176 Based 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
177 n the figure ( angle B A C=75^{circ}, angle A B C= )
( 35^{circ} . ) Find the measures of ( angle B A Z )		 9
178 Show 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
179 A 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
180 One of the angles forming a linear pair is a right angle. What can you say about its other angle? 9
181 n 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
182 If 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
183 find the value of ( x ) in each of the
following figures.
(a)		 9
184 n 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
185 What do you mean by linear pair of angles? 9
186 Mark 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
187 In figure, name each linear pair and
each pair of vertically opposite angles		 9
188 Find ( x ) 9
189 If 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
190 In 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
191 In 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
192 What is the measure of complementary
angle of ( 32^{circ} ? )
A ( cdot 48^{circ} )
B. 78
( c cdot 58 )
( D cdot 68 )		 7
193 Find 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
196 Write all pairs of vertically opposite
angles.		 9
197 n fig, if ( boldsymbol{A B}|boldsymbol{C D}, boldsymbol{C D}| boldsymbol{E F} ) and ( boldsymbol{y} )
( z=3: 7 ) find ( x )		 7
198 If 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
199 Read 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
200 If true then enter 1 and if false then
enter 0
Can two obtuse angles be
supplementary?		 7
201 Find the value of unknown ( x ) in the
following diagram.		 9
202 In 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
203 n 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
204 State true or false:
Angles forming a linear pair are supplementary.
A. True
B. False		 7
205 Find 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
206 Mark 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
207 in the given figure sides of the angles
are parallel. Find ( boldsymbol{x} ) and ( boldsymbol{y} ) if ( angle boldsymbol{A}=mathbf{5 5}^{circ} )		 9
208 The 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
209 Find the ( x ) and ( y ) in the following figure: 9
210 If ( 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
211 If true then enter 1 and if false then
enter 0

Can an acute angle be adjacent to an obtuse angle?

 9
212 In the figure, find ( x ) 7
213 As 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
214 Observe the angles shown in the figure
and write the following pair of angles.
(1) Interior alternate angles
(2) Corresponding angles
(3) Interior angles		 7
215 In the figure, if linel ( | ) m. What is the
value of ( x )		 7
216 Lines ( 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
217 The 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
218 In 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
219 The 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
220 In 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
221 In 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
222 In 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
223 In 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
224 In fig name all the pairs of adjacent angles. 9
225 Choose 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
226 If true then enter 1 and if false then
enter 0
Can two adjacent angles be
complementary?		 7
227 If ( 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
228 Measure of one angle of linear pair is
( 108^{circ}, ) then find the measure of another angle.		 9
229 Find the value of the unknown interior
angle ( x ) in the following figure.		 9
230 In the adjoining figure, identify the pair of corresponding angles 9
231 Two 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
233 fray ( 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
234 Find the measure of the complementary
angle of ( 90^{circ} )
A ( cdot 0^{circ} )
B . 45
( c .90 )
D. 60		 7
235 One angle of linear pair is a right angle, then find the measure of another angle. 9
236 Which 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
237 Which 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
238 Draw 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
240 The 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
241 Angles ( 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
242 Construct the following angles using
set-squares: ( 150^{circ} )		 9
243 Name the pairs of adjacent angles in
the figures.		 9
244 An 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
245 Find the value of ( x ) 9
246 Can two angles be supplementary if both of them are: (i) acute (ii) obtuse
(iii) right?		 7
247 Find 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
248 If 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
249 Find 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
251 13. In the given figure, find a+b+c+d.
60°
s
800
120° 		7
252 Manasa says, Each angle in any pair of complementary angles is a always
acute. Do you agree? Give reason.		 7
253 In 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
255 If true then enter 1 and if false then
enter 0

Can two obtuse angles form a linear pair?

 9
256 If 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
257 61. 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
258 In 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
259 Find 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
260 In 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
261 Two 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
262 In 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
263 In 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
264 Find ( 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
265 Find 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
266 Find the value of ( x ) in each of the
following figures?		 9
267 In 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
268 Measure of one angle of linear pair is given. Find the measure of another
angle:
( 111^{circ} )		 9
269 Find the values of the unknown ( x ) and ( y )
in the following diagram.		 9
270 IN the figure || and ( n ) is a ttansversal
such that ( angle 3: angle 8=1: 2 . ) Find ( angle 4 ) and
( angle 3 )		 7
271 Write the measure of supplementary angle of the given angles:
( mathbf{1 0 0}^{circ} )		 7
272 From 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
273 What 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
274 In 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
275 If 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
276 Identify whether the following pairs of angles are complementary or
supplementary:
( 63^{circ}, 27^{circ} )		 7
277 According to figure, find the values of
angles ( x, y ) and ( z )		 9
278 In 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
281 For an angle ( x^{2} ), find:
The supplementary angle.		 7
282 In the given figure, which line is
perpendicular to AB?
A. CD
B. EF
( c cdot G H )
( D cdot mid J )		 9
283 What are complementary and supplementary angles? 7
284 Draw 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
285 Find the complement of the angles
represented in given figure.		 7
286 n Fig., if ( boldsymbol{A B} | boldsymbol{C D} ) and ( boldsymbol{C D} | boldsymbol{E} boldsymbol{F} ), find
( angle A C E )		 7
287 Find the complementary angle of ( 45 frac{1}{2}^{circ} ) 7
288 Mark 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
289 n Fig, POQ is a line. The value of ( x ) is:
A . ( 20^{circ} )
B ( cdot 25^{circ} )
( c cdot 30^{0} )
D. 35		 7
290 By simply looking at the pair of angles
given in figure. State which of the angle
in the pairs is greater.		 9
291 If ( l | boldsymbol{m} ) and ( boldsymbol{m} | boldsymbol{n} ) then:
A . ( l | )
в. ( l | )
c. ( m | ) n
D. ( l | n )		 7
292 Lines ( 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
293 Fill 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
一较 – (1) and
(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
294 The sum of all six exterior angles of triangle is
A . 180
в. 360
c. 720
D. 90		 9
295 In 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
296 Find the value of ( x ) in each of the
following figure, if ( boldsymbol{I} | boldsymbol{m} )		 7
297 Find the value of ( x ) in each of the
following figure :		 9
298 O 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
299 Find the measure of the supplementary
angle pair of ( 60^{circ} . ) (in degrees)		 7
300 n 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
301 n figure if ( x=y ) and ( a=b, ) then prove
that ( r | n )		 7
302 Complement angle of
A . ( 77.4^{circ} )
B .67 .3
( c cdot 76.3^{circ} )
D. ( 77.3^{circ} )		 7
303 The supplement angle of the
complement of ( 30^{circ} ) is
A ( .150^{circ} )
B . ( 120^{circ} )
( mathrm{c} cdot 90^{circ} )
D. ( 210^{circ} )		 7
304 In 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
305 Find 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
306 Measure of one angle of linear pair is given. Find the measure of another
angle:
( mathbf{2 0}^{circ} )		 9
307 Three times the complement of an angle
is ( 20^{circ} ) more than its supplement. Find
the angle.		 7
308 If true then enter 1 and if false then
enter 0
Can two obtuse angles be complement
to each other?		 7
309 Find 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
310 Write down each pair of adjacent angles
shown in figure.		 9
311 OA 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
312 1.
An angle is equal to one-third of its supplement. Find its measure. 		7
313 If 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
314 Using information given in the adjacent
figure, find the values of ( x ) and ( y )		 9
315 Let 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
316 Mark 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
318 Twp 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
319 If 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
320 From 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
322 If 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
323 Lines ( 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
324 In the adjoining figure, name the
following pairs of angles.
Equal supplementary angles		 7
325 In 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
326 n fig. I I I and p I Find values of ( x, y )
( z, t )		 9
327 Measure of one angle of linear pair is given. Find the measure of another
angle:
( mathbf{1 0 7}^{circ} )		 9
328 In 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
329 Find the value of unknown ( x ) in the
following diagram		 9
330 In each of the following figure ( A B | C D ) Find the value of ( x ) in each case 7
331 n 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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