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LINES AND ANGLES
1. In the given figure, POQ is a line. The value of x is:
a. 20
0
b. 25
0
c. 30
0
d. 35
0.
2. An exterior angle of a triangle is 110
0
and its two interior opposite angles are equal. Each
of these equal angles is:
a. 45
0
b. 50
0
c. 55
0
d. 75
0
3. 𝐼𝑛 ∆ 𝐴𝐵𝐶 , 𝐵𝐶 = 𝐴𝐵 𝑎𝑛𝑑 ∠ 𝐵 = 80
0
. 𝑇ℎ𝑒𝑛 ∠ 𝐴 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 :
a. 40
0
b. 50
0
c. 80
0
d. 100
0
4.
𝐼𝑛 ∆ 𝐴𝐵𝐶 , 𝐴𝐵 = 𝐴𝐶 𝑎𝑛𝑑 ∠ 𝐵 = 50
0
, 𝑡ℎ𝑒𝑛 ∠ 𝐴 =
a. 150
0
b. 120
0
c. 60
0
d. 80
0
5. An exterior angle of a triangle is 110
0
and its two interior opposite angles are equal, each
of these equal angle is
a. 70
0
b. 55
0
c. 35
0
d. 50
0
6. An angle which measure more than 180
0
but less than 360
0
is called
a. Acute angle b. Obtuse angle c. Right angle d. A reflex angle
7. The measure of an angle is 45
0
, find its complement.
a. 45
0
b.50
0
c. 60
0
d. 90
0
8.
𝐼𝑛 ∆ 𝐴𝐵𝐶 , 𝐵𝐶 = 𝐴𝐵 𝑎𝑛𝑑 ∠ 𝐵 = 80
0
𝑡ℎ𝑒𝑛 ∠ 𝐴 =?
a. 50
0
b. 40
0
c. 100
0
d. 80
0
9. Which is true?
a. A triangle can have two right angles
b. A triangles can have two obtuse angle
c. A triangle can have two acute angle
d. Any one of these.
10. A reflex angle is an angle whose measure:
a. More than 90
0
b. Equal to 90
0
c. More than 180
0
d. Equal to 180
0
11. The measure of an angle is five times its complement. The measure of the angle is
a. b. c. d.
25
0
35
0
65
0
75
0
12. In figure , the value of x is:-
𝑙
1
∥ 𝑙
2
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a. b. c. d.
100
0
80
0
110
0
70
0
13. In figure, find the value of y :-
a. b. c. d.
28
0
40
0
140
0
56
0
14.
𝐼𝑛 ∆ 𝐴𝐵𝐶 𝑎𝑛𝑑 𝑖𝑓 𝐴𝐵 = 𝐴𝐶 , ∠ 𝐵 = 40
0
. 𝑇ℎ𝑒𝑛 ∠ 𝐶 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜
a. b. c. d.
50
0
40
0
80
0
140
0
15. Choose the correct statement:-
a. A triangle has two right angles
b. All the angles of a triangle are more than 60
o
.
c. An exterior angle of a triangle is always greater than the opposite interior angles.
d. All the angles of a triangle are less than
16. In an isosceles triangle, the angles opposite to equal sides are:
a. Right angles b. Acute angles c. Obtuse angles d. Equal angles
17. Two straight lines AB and CD cut each other at O. If ∠BOD = 63
0
then ∠BOC = ?
a. 63
0
b. 117
0
c. 17
0
d. 153
0
18. In , if ∠A+∠B =125
0
and ∠A+∠C = 113
0
then ∠A = ?
∆ 𝐴𝐵𝐶
a. 62.5
0
b. 56.5
0
c. 58
0
d. 63
0
19. The angles of a triangle are in the ratio 3:5:7, the triangle is :
a. Acute angled triangle
b. Right angled triangle
c. Isosceles triangle
d. Obtuse angled triangle
20. An exterior angle of a triangle is 110
0
and its two interior opposite angles are equal, each
of these angle is
a. 70
0
b. 55
0
c. 35
0
d. 50
0
21. If two angles are complement of each other then each angle is
a. Acute angle b. Obtuse angle c. right angle d. Reflex angle
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22. The measure of an angle is 45
0
. Find its complement.
a. 45
0
b. 50
0
c. 60
0
d. 90
0
23. In ABC, BC = AB and ∠B = 80
0
then ∠A = ?
∆
a. 50
0
b. 40
0
c. 100
0
d. 80
0
24. In Fig, if AB || CD, EF ⊥ CD and ∠ GED = 126°, find ∠ AGE.
a. 120
0
b. 140
0
c. 90
0
d. 135
0
25. Side BC of a has been produced to a point D such that ∠ACD = 120
0
if ∠B = ∠A
∆ 𝐴𝐵𝐶
1
2
then ∠A = ?
a. 80
0
b. 75
0
c. 60
0
d. 90
0
26. Two straight lines AB and CD cut each other at O. If ∠BOD = 63
0
, then ∠BOC = ?
a. 63
0
b. 117
0
c. 17
0
d. 153
0
27.
𝐼𝑛 ∆ 𝐴𝐵𝐶 𝑎𝑛𝑑 𝑖𝑓 𝐴𝐵 = 𝐴𝐶 , ∠ 𝐵 = 40
0
. 𝑇ℎ𝑒𝑛 ∠ 𝐶 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜
a. b. c. d.
50
0
40
0
80
0
140
0
28. Opposite angles of a parallelogram are …………
29.
𝐼𝑛 𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 , 𝑙𝑖𝑛𝑒𝑠 𝑋𝑌 𝑎𝑛𝑑 𝑀𝑁 𝑖𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡 𝑎𝑡 𝑂 . 𝐼𝑓 ∠ 𝑃𝑂𝑌 = 90
0
𝑎𝑛𝑑 𝑎 : 𝑏 = 2 : 3 , 𝑓𝑖𝑛𝑑 𝑐 .
30. In the figure, line AB and CD intersect at O. If AOC + BOE = 80
0
and BOD = 30
0
,
∠ ∠ ∠
find BOE and reflex COE.
∠ ∠
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31. In figure, if PQ ∥ ST, PQR = 110
0
and RST = 130
0
, find QRS.
∠ ∠ ∠
32. In figure, if AB ∥ DE, BAC = 35
0
and CDE = 53
0
, find DCE.
∠ ∠ ∠
33. In the figure, POQ is a line, Ray OR is perpendicular to line PQ. OS is another ray lying
between rays OP and OR. Prove that ROS = ½( QOS - POS).
∠ ∠ ∠
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34. In the figure, if AB ∥ CD, EF CD and GED = 126
0
, find AGE, GEF and FGE.
⊥ ∠ ∠ ∠ ∠
35. Prove that the sum of three angles of a triangle is 180
0
.
36. Prove that an exterior angle of a triangle is equal to the sum of two interior opposite
angles of a triangle.
37.
𝐼𝑓 𝐴𝐵 ∥ 𝐶𝐷 ∥ 𝐸𝐹 , 𝑓𝑖𝑛𝑑 𝑥 𝑖𝑛 𝑡ℎ𝑒 𝑔𝑖𝑣𝑒𝑛 𝑓𝑖𝑔𝑢𝑟𝑒 .
38. Prove that angles opposite to equal sides in an isosceles triangle are equal.
39. such that
∆ 𝐴𝐵𝐶 𝑖𝑠 𝑎𝑛 𝑖𝑠𝑜𝑠𝑐𝑒𝑙𝑒𝑠 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑖𝑛 𝑤ℎ𝑖𝑐ℎ 𝐴𝐵 = 𝐴𝐶 . 𝑆𝑖𝑑𝑒 𝐵𝐴 𝑖𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑡𝑜 𝐷
AD=AB. Show that BCD is a right triangle.
∠
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40. Each angle of an equilateral triangle measure is ………..
41. Median of an equilateral triangle are ……………
42. In a right angled triangle the hypotenuse is the ……….. Side.
43. Define:
a. Complementary angles
b. Supplementary angles
c. Linear pair of angle
44. Prove that the angles opposite to equal sides of an isosceles triangle are equal.
45. Find the angle which is four times its complement.
46. and AB=AC find B and C.
𝐴𝐵𝐶 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒𝑑 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑖𝑛 𝑤ℎ𝑖𝑐ℎ ∠ 𝐴 = 90
0
∠ ∠
47. In Fig, if AB || CD, ∠ APQ = 50° and ∠ PRD = 127°, find x and y
48. Show that the angle of an equilateral triangle is 60
0
.
49. In fig, AB || CD and CD || EF also EA AB if ∠BEF=55
0
find the value of x, y and z.
⊥
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50. In Fig, the sides AB and AC of ∆ABC are produced to points E and D respectively. If
bisectors BO and CO of ∠ CBE and ∠ BCD respectively meet at point O, then prove that
.
∠ 𝐵𝑂𝐶 = 90
0
−
1
2
∠ 𝐵𝐴𝐶
51.
𝐼𝑓 ( 3 𝑥 − 15 )
0
𝑎𝑛𝑑 𝑥 + 5 ( )
0
𝑎𝑟𝑒 𝑐𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 𝑎𝑛𝑔𝑙𝑒𝑠 , 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑎𝑛𝑔𝑙𝑒𝑠
52.
𝐼𝑛 𝑡ℎ𝑒 𝑔𝑖𝑣𝑒𝑛 𝑓𝑖𝑔𝑢𝑟𝑒 , 𝐴𝐵 ∥ 𝑃𝑄 . 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑥 𝑎𝑛𝑑 𝑦 .
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53. In the figure, AB ∥ CD and a transversal cuts AB and CD at A and C respectively.
Bisectors of ∠A and ∠C intersects each other at P. Prove that ∠PAC = 90
0
.
54. In Fig, if x + y = w + z, then prove that AOB is a line.
55. Prove that if two lines intersect then vertically opposite angles are equal.
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56. In Fig, if PQ ⊥ PS, PQ || SR, ∠ SQR = 28° and ∠ QRT = 65°, then find the values of x
and y.
57. Find the value of x in each case:-
a.
b.
58. Can a triangle have two obtuse angles ? Give reason for your answer.
59. Prove that the sum of the angles of a triangle is 180
0
.
60. ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.
61. In a right angled triangle the hypotenuse is the …………… side.
62. Define :-
a. Parallel lines
b. Line segment
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c. Complementary angles
d. Supplementary angles
e. Linear pair of angle
63. Angles opposite to equal sides of an isosceles triangle are equal, prove it.
64. ABC is right angled triangle in which ∠A = 90
0
and AB = AC find ∠B and ∠C.
65. Write the angle sum property of the triangle and prove it.
66. Write the exterior angle property of the triangle and prove it.
67. Show that the angles of an equilateral triangle is 60
0
.
68. In the given figure, if PQ∥RS, ∠MXQ = 135
0
, ∠MYR = 40
0
, find ∠XMY.
69. If the bisector of the exterior angle of a ABC is parallel to the side AB, then prove that
∆ ∆
ABC is an isosceles triangle.
70. If a transversal intersects two parallel lines, prove that the bisectors of the interior angles
on the same side of the transversal intersect each other at right angle.
71. It is given ∠XYZ = 64 and XY is produced to point P. Draw a figure from the given
information. If a ray YQ bisects ∠ZYP find ∠XYQ and reflex ∠QYP.
72. Can a triangle have two obtuse angles ? Give reason for your answer.
73. Prove that the sum of the angles of a triangle is 180
0
.
74. Assertion: If angles ‘a’ and ‘b’ form a linear pair of angles and a = 40
0
, then b = 150
0
.
Reason: Sum of linear pair of angles is always 180
0
.
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
75. Assertion(A): If two interior angles of the same side of a transversal intersecting two
parallel lines are in the ratio 5:4, then the greater of the two angles is 100
0
.
Reason(R): If a transversal intersects two parallel lines, then the sum of the interior
angles on the same side of the transversal is 180
0
.
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
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d. Assertion (A) is false but reason (R) is true.
76. Assertion(A): Two angles measure (a-60
0
) and (123
0
-2a). If each one is opposite the
equal side of an isosceles triangle, then the value of a is 61
0
.
Reason(R): Sides opposite to equal angles of a triangle are equal.
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
77. ASSERTION : In the given figure, BO and CO are the bisectors of ∠B and ∠C
respectively. If ∠A = 50
0
then ∠BOC = 115
0
REASON: The sum of all the interior angles of a triangle is 180
0
.
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
78. ASSERTION : Angles opposite to equal sides of a triangle are not equal.
REASON: Sides opposite to equal angles of a triangle are equal.
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
79. ASSERTION : If angles ‘a’ and ‘b’ form a linear pair of angles and a = 40
0
, then b=150
0
.
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REASON: Sum of linear pair of angles is always 180
0
.
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
80. ASSERTION : In a ABC, if the bisectors of ∠B and ∠C meet at O, then ∠BOC is always
∆
an obtuse angle.
REASON: In a ABC, f the bisectors of ∠B and ∠C meet at O, then ∠BOC =
∆
.
90
0
+
1
2
∠ 𝐴
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
81. Assertion (A): An angle is 14
0
more than its complementary angle, then angle is 52
0
Reason (R): Two angles are said to be supplementary if their sum of measure of
angles is 180
0
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
82. OA, OB, OC, OD, OE and OF are six roads and all join at a point ‘O’. These roads make
angles (∠a, ∠b, ∠c, ∠d and ∠e) according to the figure. Roads OD and OE are
perpendicular to each other. AD and CF are straight lines and intersect each other at ‘O’.
∠a, ∠b and ∠c are in the ratio 2:3:4. A teacher showed this figure to a mathematics
student and asked the following question. Now using the given information, answer
these questions : -
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a. Find the measure of ∠a
b. Find the measure of ∠d and ∠c
c. FInd ∠b + reflex ∠c
d. Find the complement and supplement of ∠c
83. Math teacher draws a straight line AB shown on the blackboard as per the following
figure:
Now he told Raju to draw another line CD as is the figure, the teacher told Ajay to mark
∠AOD as 2z, Suraj was told to mark ∠AOC as 4y, Clive made and angle ∠COE = 60
0
,
Peter marked ∠BOE and ∠BOD as y and x respectively.
Now answer the following questions:
1. What is the value of x?
2. What is the value of y?
3. What is the value of z?
84. Once 4 students from class IX F were selected for the planting of flower plants in the
school garden. The selected students were Pankaj, Raju, Deepak and Renu. As shown
PQ and MN are the parallel lines of the plants. Pankaj planted a sunflower plant at P,
then Raju planted another sunflower at Q. Further, Deepak was called to plant any
flowering plant at point M. He planted a marigold there. Now it was the turn of Renu. She
was told to plant a flowering plant different from the three planted one So she planted a
