1. In the given figure, the value of x which makes POQ a straight line is:

(a) 35 (b) 30 (c) 25 (d) 40

2. The angle which is equal to 8 times its complement is :

(a) 80°

(b) 72°

(c) 90°

(d) 88°

3. In the figure, if m||n and Ða : Ðb = 2 : 3,

then measure of Ð h is :

(a) 72° (b) 108° (c) 120° (d) 150°

4. In the figure, value of x is :

(a) 50° (b) 40° (c) 60° (d) 70°

5. An exterior angle of a triangle is 80° and the interior opposite angles are in the ratio 1 : 3. Measure of each interior opposite angle is :

(a) 30°, 90° (b) 40°, 120°

(c) 20 °, 60°

(d) 30°, 60°

6. The complementary angles are in the ratio 1 : 5. Find the measures of the angles :

(a) 15°, 75° (b) 75°, 15°

(c) 12°, 60° (d) 60°, 12°

7. In the given figure, l || m || n, If x : y = 5 : 4, then the measure of angle z is :

(a) 40° (b) 50° (c) 90° (d) 80°

8. The complement of an angle m is :

(a) m (b) 90° + m

(c) 90° – m (d) m × 90°

9. If the measure of an angle is twice the measure of its supplementary angle, then the measure of the angle is :

(a) 60° (b) 90°

(c) 120° (d) 130°

10. If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3, then the larger of two angles is :

(a) 72° (b) 108° (c) 54° (d) 36°

11. In the given figure, if PQ||RS, then the measureof m is :

(a) 110° (b) 100° (c) 90° (d) 137°

LINES and ANGLESCLASS IX

Questions From CBSE Examination Papers

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12. In the given figure, PQ||RS and EF||QS. IfÐPQS=60°,then the measure of ÐRFE is :

(a) 115° (b) 120° (c) 60° (d) 180°

13. In the figure, AB||CD,the value of x is :

(a) 35° (b) 40° (c) 60° (d) 75°

14. In the figure, AB and CD are parallel to each other.The value of x is :

(a) 90° (b) 100°

(c) 120° (d) 140°

15. Find the measure of the angle which is complement of it self.

(a) 30° (b) 90°

(c) 45° (d) 180°

16. Two lines are respectively perpendicular to two perpendicular lines. Then these two lines to each other are :

(a) parallel

(b) perpendicular

(c) inclined at same acute angle

(d) intersecting at 110 °

17. In the figure, lines AB and CD intersect at O. IfÐAOD : ÐDOB = 4 : 5, then ÐCOB is :

(a) 80° (b) 100° (c) 90° (d) 70°

18. In the figure, the value of x is :

(a) 30° (b) 10° (c) 20° (d) 40°

19. Measure of an angle which is supplement to itself is :

(a) 45° (b) 30° (c) 90° (d) 180°

20. In the figure, valueof x is :

(a) 20° (b) 40° (c) 30° (d) 50°

21. Given lines l1, l

2 and l

3in figure areparallel.The

value of x is :

(a) 40° (b) 140° (c) 50° (d) 80°

22. The complement of (90 ° – a) is :

(a) – a° (b) 90° + a (c) 90° – a (d) a°

23. In the figure, AB||CD and t is a transversal, the value of x is equal to :

(a) 50° (b) 70° (c) 35° (d) 20°

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24. If l, m, n are lines in the same plane such that l intersects m and n||m, then l and n are :

(a) parallel

(b) intersecting

(c) always perpendicular

(d) always intersecting at 60°

25. If two supplementary angles are in the ratio 2 : 7, then the angles are :

(a) 35° 145° (b) 70°, 110°

(c) 40 °, 140° (d) 50°, 130°

26. From thefigure, identify the incorrect statement, giventhat l ||m and t is the transversal.

(a) Ð2 and Ð5 are supplementary

(b) Ð2 and Ð3 are supplementary

(c) Ð2 and Ð8 are supplementary

(d) Ð2 and Ð1 are supplementary

27. In the figure, PQ||RS, ÐQPR=70°, ÐROT = 20°. Find the value of x.

(a) 20° (b) 70° (c) 110° (d) 50°

28. In the figure, l1||l

2. The value of x is :

(a) 70° (b) 30° (c) 40° (d) 50°

29. In the given figure, the measure of ÐABC is :

(a) 80° (b) 20° (c) 100° (d) 60°

30. In the figure, if x°, y° and z° are exterior angles of DABC, then x° + y° + z° is :

(a) 180° (b) 360° (c) 270° (d) 90°

31. The angles of a triangle are in the ratio 2 : 3 : 4. The angles are :

(a) 20°, 60 °, 80° (b) 80°, 40°, 60°

(c) 40°, 60 °, 80° (d) 60°, 40°, 80°

32. In a triangle ABC, if ÐA = 53° and ÐC = 44°, then the value of ÐB is :

(a) 73° (b) 83° (c) 93° (d) 46°

33. In the figure, the value of( Ðx + Ðy) is :

(a) 80° (b) 100° (c) 120° (d) 60°

34. In the figure, if AB=AC, find x.

(a) 55° (b) 110° (c) 50° (d) 70°

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35. In the figure,the value of x is :

(a) 120° (b) 130° (c) 110° (d) 100°

36. In the figure, measure of ÐABC is :

(a) 60° (b) 70° (c) 80° (d) 50°

37. An exterior angle of a triangle is 80 ° and the interior opposite angles are in the ratio 1 : 3. Measure of each interior opposite angle is :

(a) 30°, 90° (b) 40°, 120°

(c) 20 °, 60° (d) 30°, 60°

38. In the figure, the value of y is :

(a) 28° (b) 32° (c) 36° (d) 44°

39. In the figure, l1||l

2, the value of x is :

(a) 80° (b) 100° (c) 110° (d) 70°

40. In the figure, ray OC stands on the lineAB, rayOL and ray OM are angle bisectors of ÐAOC and ÐBOC respectively. Prove that ÐLOM = 90°.

41. In the figure, PQ||SR, ÐSQR=25°, ÐQRT=65°,find x and y :

42. In the figure, if PQ||RS, ÐPAB=60° and ÐACS =117°,then find (x – y).

43. If x + y = s + w, prove that AOB is a straight line.

44. In the figure,find the values of x and y.

45. In the figure, OA,OB are opposite rays and ÐAOC + ÐBOD = 90°. Find ² COD.

46. In the figure, if a ray OC stands on line AB suchthat ÐAOC = ÐCOB, then show that ÐAOC = 90°.

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47. If two lines are perpendicular to the same line, prove that they are parallel to each other.

48. In the figure, if AB||CD, then find ÐPQR.

49. In the figure, if AB||DE, then find the measure ofÐBCD.

50. In the figure, OQ bisects ÐAOB. OP is a rayoppositetoray OQ. Prove that ÐPOA= ÐPOB.

51. In the figure, fnd x and y and then show that AB||CD.

52. In the figure, AB||DE, ÐABC = 75° and ÐCDE =145°,then find ÐBCD.

53. In the figure, PQ||RS, ÐPAB=70°and ÐACS = 100°. Find the value of x.

54. If OA, OB, OC and OD are the rays such that ÐAOB = ÐCOD = 150°, ÐBOC = 30° and ÐAOD = 30°. Is it true that AOC and BOD are straight lines ? Justify your answer.

55. Lines PQ and RS intersecteachotheratpointO.If ÐPOR: ÐROQ = 5:7,find all the remainingangles.

56. In the figure, lines l and m intersect each other at O. If x=40°,then fnd the values of y, z and w.

57. If l, m, n are three lines such that l || m and n l, then prove that n m .

58. In the figure, find the values of x and y and then show that AB||CD.

59. In the figure, PQ||RS, ÐPAB=80°and ÐACS = 120°. Find the value of x.

60. If the complement of an angle is one-third of its supplement, find the angle.

61. In the figure, if AB||CD, then fnd the value ofx.

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62. In the figure, if ÐPQR= ÐPRQ,then prove thatÐPQS= ÐPRT.

63. In the figure, x = 61° and y = 118°. Is m||n ?

64. In the figure, if x ¹ y = w + z, then prove that AOB is a line.

65. In the figure, ÐPOQ and ÐROQ form a linearpair. Find the measure of x.

66. In the figure, AB||CD, find the value of x.

67. In the figure, find the value of x.

70. In the given figure, if l || m, then find the valueof x.

AB and CD are the bisectors of the two alternate interior angles formed by the intersection of a transversal t with parallel lines l and m (shown in the figure). Show that AB||CD.

68. In the figure, find the value of ÐQRP whenQP||TR.

69. In the figure, prove that AB||EF.

`

71.

72. In the figure, if y = 20°, prove that the line AOB is a straight line.

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73. In the figure, ray OS standson a line POQ. RayOR and ray OT are angle bisectors of ÐPOSandÐSOQ respectively. If ÐPOS= x, find ÐROT.

74. In the figure, if AB||CD, ÐAPQ =50°and ÐPRD=127°, find x and y.

75. Prove that if two lines intersect, the verticallyopposite angles are equal.

76. In the figure, if PQ||RS and ÐPXM = 50° andÐMYS=120°,find the value of x.

77. In the figure, l1

|| l2 and m

1 || m

2

Prove that Ð1 + Ð2 = 180°

78. In the figure, if x : y=3:7,then find the valuesof x, y, z and w.

79. In the figure, lines AB and CD are parallel andP is any point between the two lines. Prove thatÐDPB= x + y.

80. In the figure, AB||CD, CD||EF and y : z = 3 : 7, find the measures of x, y and z.

81.

82.

83.

84.

In the figure, AB||CD and CD||EF. Also EA AB. If ÐBEF=55°, find the values of x, y and z.

In the figure, if AB||CD, ÐFAE = 90° and ÐAFE =40°, then find ÐECD.

In the figure, PQ||RS and T is any point as shownin the figure, then show that ÐPQT + ÐQTS +ÐRST = 360°.

In t he figure,POQ is a line, ray OR is perpendicularto line PQ.OS is another ray lying between rays

OP and OR. Prove that ÐROS = 1

2 (ÐQOS– ÐPOS)

85. In the figure, l1 || l

2 and a

1 || a

2. Find the value of x.

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86. In the figure,find the value of x

87. In the figure,prove that l || m.

88. In the figure, prove that AB||EF.

89. In the figure, show that AB||EF.

90. In

In

the figure, OP bisects ÐAOC, OQ bisectsÐBOC and OP OQ. Show that pointsA, O and B arecollinear.

91. P is a point equidistant from two lines l and m intersecting at a point A. Show that AP bisects theangle between them.

92. In the figure, two straight lines AB and CD intersecteach other at O. If ÐCOE=70°,find the valuesofa , b and c.

93. the figure, l || m, show that Ð1 + Ð2 – Ð3 = 180°

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