EduSahara™ Worksheet

Question 1

1.

(i)

152.5°
(ii)

142.5°
(iii)

167.5°
(iv)

147.5°
(v)

137.5°

Question 2

2.

O is the centre of the circle. If ∠BOD = 89°, find ∠A

(i)

59.5°
(ii)

74.5°
(iii)

49.5°
(iv)

54.5°
(v)

44.5°

Question 3

3.

O is the centre of the circle. If ∠GOF = 107° and ∠HOF = 113°, find ∠GFH

(i)

70°
(ii)

85°
(iii)

80°
(iv)

75°
(v)

100°

Question 4

4.

Find the missing angle in the following figure?

(i)

57°
(ii)

27°
(iii)

32°
(iv)

37°
(v)

42°

Question 5

5.

O is the centre of the circle and OC = BC. Find ∠BOC

(i)

65°
(ii)

60°
(iii)

90°
(iv)

75°
(v)

70°

Question 6

6.

O is the centre of the circle and OI = HI. Find ∠IOG

(i)

135°
(ii)

150°
(iii)

130°
(iv)

125°
(v)

120°

Question 7

7.

O is the centre of the circle and OF = EF. Find reflex ∠FOD

(i)

245°
(ii)

250°
(iii)

270°
(iv)

255°
(v)

240°

Question 8

8.

(i)

83°
(ii)

78°
(iii)

108°
(iv)

93°
(v)

88°

Question 9

9.

O is the centre of the circle. If ∠DFE = 45° and ∠FDG = 51°, find u°, v°

(i)

70°, 65°
(ii)

50°, 55°
(iii)

30°, 45°
(iv)

40°, 45°
(v)

45°, 40°

Question 10

10.

O is the centre of the circle. If ∠EOF = 148°, find the angle ∠G

(i)

84°
(ii)

79°
(iii)

74°
(iv)

104°
(v)

89°

Question 11

11.

Two circles touch internally. L is the centre of the bigger circle and lies on the smaller circle. If ∠IJK = 48°, find ∠I

(i)

42°
(ii)

47°
(iii)

57°
(iv)

72°
(v)

52°

Question 12

12.

△LMN is inscribed in a circle with centre O. If ∠LOM = 137° and ∠MON = 158°, find ∠NLM

(i)

89°
(ii)

109°
(iii)

94°
(iv)

79°
(v)

84°

Question 13

13.

△FGH is inscribed in a circle with centre O. If ∠FOG = 138° and ∠GOH = 165°, find ∠FGH

(i)

58.5°
(ii)

43.5°
(iii)

28.5°
(iv)

33.5°
(v)

38.5°

Question 14

14.

△EFG is inscribed in a circle with centre O. If ∠EOF = 145° and ∠FOG = 154°, find ∠FGE

(i)

72.5°
(ii)

77.5°
(iii)

82.5°
(iv)

87.5°
(v)

102.5°

Question 15

15.

In the given figure, O is the centre of the circle. If ∠FIG = 53.5° and ∠OFI = 30°, find ∠HGI

(i)

120°
(ii)

130°
(iii)

150°
(iv)

125°
(v)

135°

Question 16

16.

In the given figure, O is the centre of the circle and GH is a diameter. If ∠HOJ = 92°, find ∠GIJ

(i)

49°
(ii)

59°
(iii)

54°
(iv)

44°
(v)

74°

Question 17

17.

In the given figure, O is the centre of the circle and FH is a diameter. If ∠GEF = 64°, find ∠GFH

(i)

36°
(ii)

31°
(iii)

26°
(iv)

41°
(v)

56°

Question 18

18.

In the given figure, O is the centre of the circle and CE is a diameter. If ∠BOE = 100° and ∠OED = 61°, find ∠CDB + ∠DCE

(i)

69°
(ii)

99°
(iii)

79°
(iv)

84°
(v)

74°

Question 19

19.

In the given figure, O is the centre of the circle and IK is a diameter. If ∠HJI = 30° and ∠IHJ = 62°, find ∠KIJ + ∠HJK

(i)

118°
(ii)

98°
(iii)

103°
(iv)

93°
(v)

88°

Question 20

20.

In the given figure, O is the centre of the circle. If ∠KJL = 49° and ∠JLM = 32°, find ∠LNM

(i)

99°
(ii)

104°
(iii)

129°
(iv)

114°
(v)

109°

Question 21

21.

O is the centre of the circle. If Arc BD = 2 Arc DE and ∠BOD = 74°, find ∠BED

(i)

37°
(ii)

42°
(iii)

67°
(iv)

52°
(v)

47°

Question 22

22.

O is the centre of the circle. If Arc DF = 2 Arc FG and ∠DOF = 73°, find ∠GDF

(i)

18.2°
(ii)

23.2°
(iii)

48.2°
(iv)

28.2°
(v)

33.2°

Question 23

23.

O is the centre of the circle. If Arc EG = 2 Arc GH and ∠EOG = 71°, find ∠EFG

(i)

159.5°
(ii)

174.5°
(iii)

149.5°
(iv)

144.5°
(v)

154.5°

Question 24

24.

In the given figure, FG is a side of regular 9-sided polygon and FH is a side of regular 5-sided polygon inscribed in a circle with centre O. Find ∠FOG

(i)

55°
(ii)

45°
(iii)

50°
(iv)

40°
(v)

70°

Question 25

25.

In the given figure, IJ is a side of regular 10-sided polygon and IK is a side of regular 8-sided polygon inscribed in a circle with centre O. Find ∠IKJ

(i)

33°
(ii)

18°
(iii)

23°
(iv)

48°
(v)

28°

Question 26

26.

In the given figure, DE is a side of regular 10-sided polygon and DF is a side of regular 9-sided polygon inscribed in a circle with centre O. Find ∠DEF

(i)

50°
(ii)

25°
(iii)

20°
(iv)

35°
(v)

30°

Question 27

27.

In the given figure, O is the centre of the circle, and OJ ⟂ FG. If ∠FGH = 36.5°, find ∠FOH

(i)

88°
(ii)

103°
(iii)

78°
(iv)

83°
(v)

73°

Question 28

28.

In the given figure, O is the centre of the circle, and OH ⟂ DE. If ∠DEF = 43°, find ∠OGF

(i)

77°
(ii)

47°
(iii)

52°
(iv)

57°
(v)

62°

Question 29

29.

In the given figure, O is the centre of the circle. If ∠HFG = 49.87° and ∠FGH = 77.4°, find the angle ∠FIG

(i)

82.73°
(ii)

67.73°
(iii)

52.73°
(iv)

57.73°
(v)

62.73°

Question 30

30.

Which of the following statements are true?

a)	Angles in the opposite segments are complementary.
b)	Angles subtended by equal length arcs in two circles are equal.
c)	Angles in the same segment are equal.
d)	Angles in the opposite segments are supplementary.

(i)

{b,d}
(ii)

{c,d}
(iii)

{a,c}
(iv)

{a,b,c}
(v)

{a,d,c}

Question 31

31.

If an arc subtends an angle of x° in its alternate segment, then the angle is subtends at the centre is

(i)

4x°
(ii)

x°

2
(iii)

2x°
(iv)

x°

Question 32

32.

An arc subtends 90° in its alternate segment. The arc is

(i)

minor segment
(ii)

major segment
(iii)

quadrant
(iv)

semi-circle
(v)

minor arc

Question 33

33.

An arc subtends 147° in its alternate segment. The arc is

(i)

quadrant
(ii)

major segment
(iii)

semi-circle
(iv)

minor segment
(v)

major arc

Question 34

34.

An arc subtends 52° in its alternate segment. The arc is

(i)

semi-circle
(ii)

minor segment
(iii)

minor arc
(iv)

major arc
(v)

quadrant

Question 35

35.

An arc subtends 31° in its alternate segment. Its corresponding major arc subtends what angle in its (major arc) alternate segment?

(i)

164°
(ii)

159°
(iii)

179°
(iv)

149°
(v)

154°

Question 36

36.

An arc subtends 51° in its alternate segment. The angle made by its corresponding major arc at the centre is

(i)

273°
(ii)

258°
(iii)

288°
(iv)

268°
(v)

263°

Question 37

37.

The angle subtended by the semicircle at the centre is

(i)

190°
(ii)

195°
(iii)

210°
(iv)

180°
(v)

185°

Question 38

38.

The angle subtended by the diameter at any point on the circle is

(i)

100°
(ii)

120°
(iii)

90°
(iv)

105°
(v)

95°

Question 39

39.

Angle subtended by the major arc at the centre is

(i)

reflex angle
(ii)

complete angle
(iii)

straight angle
(iv)

right angle
(v)

acute angle

Question 40

40.

Angle subtended in the major segment is

(i)

complete angle
(ii)

acute angle
(iii)

reflex angle
(iv)

right angle
(v)

zero angle

Question 41

41.

In the given figure, FG & HI are diameters of the circle. If ∠FGH = 34° find, ∠GOH

(i)

127°
(ii)

122°
(iii)

142°
(iv)

112°
(v)

117°

Question 42

42.

In the given figure, EF & GH are diameters of the circle. If ∠EHG = 23°, find ∠OGF

(i)

53°
(ii)

28°
(iii)

38°
(iv)

23°
(v)

33°

Question 43

43.

In the given figure GI & HI are equal length chords of the circle. Find ∠IGH

(i)

50°
(ii)

55°
(iii)

75°
(iv)

45°
(v)

60°

Question 44

44.

In the given figure, JK is a diameter of the circle with centre O. If ∠KJL = 53.84° and KL = KM, find ∠MLJ

(i)

46.16°
(ii)

66.16°
(iii)

36.16°
(iv)

51.16°
(v)

41.16°

Question 45

45.

In the given figure, O is the centre of the circle. If ∠ODF = 36°, find ∠E

(i)

156°
(ii)

126°
(iii)

131°
(iv)

141°
(v)

136°

Question 46

46.

In the given figure, O is the centre of the circle. If ∠FGH = 139°, find ∠OFH

(i)

79°
(ii)

54°
(iii)

49°
(iv)

59°
(v)

64°

Question 47

47.

O is the centre of the circle. If ∠FGE = 37°, find the angle ∠OFE

(i)

68°
(ii)

58°
(iii)

83°
(iv)

53°
(v)

63°

Question 48

48.

GH is the perpendicular bisector of side EF of △DEF. Given ∠DEF = 46° and ∠GDF = 49° , find ∠DFE

(i)

36°
(ii)

51°
(iii)

66°
(iv)

41°
(v)

46°

Question 49

49.

In the given figure, △LIJ is a scalene triangle. KI bisects ∠LIJ. Similarly JK bisects ∠IJL. Given ∠JLI = 110°, find ∠JKI

(i)

175°
(ii)

160°
(iii)

145°
(iv)

155°
(v)

150°

Question 50

50.

In the given figure, △KGH is a scalene triangle. IG & JG trisect ∠KGH. Similarly HI & HJ trisect ∠GHK. Given ∠HKG = 75°, find ∠HIG

(i)

150°
(ii)

155°
(iii)

175°
(iv)

160°
(v)

145°

Question 51

51.

In the given figure, △EAB is a scalene triangle. CA & DA trisect ∠EAB. Similarly BC & BD trisect ∠ABE. Given ∠BEA = 87°, find ∠BDA

(i)

133°
(ii)

148°
(iii)

118°
(iv)

123°
(v)

128°

Question 52

52.

In the given figure, ∠EGH = 10° and ∠EIH = 38°, find ∠GEH

(i)

47°
(ii)

72°
(iii)

42°
(iv)

57°
(v)

52°

Question 53

53.

In the given figure, ∠CEF = 15° and ∠CGF = 29°, find ∠DFC

(i)

105°
(ii)

80°
(iii)

85°
(iv)

75°
(v)

90°

Question 54

54.

In the given figure, JL is a chord which is equal to the radius of the circle. Find ∠M and ∠K

(i)

30° & 150°
(ii)

40° & 140°
(iii)

50° & 130°
(iv)

60° & 120°
(v)

45° & 135°

Question 55

55.

Which of the following statements are true?

a)	If two chords are equal, then they are equidistant from the centre of the circle.
b)	Angle subtended by the major arc in its alternate segment is obtuse.
c)	Angle subtended in the major segment is obtuse.
d)	Angle subtended by the major arc at the centre is acute.
e)	The angle subtended in a semicircle is a right angle.

(i)

{c,a}
(ii)

{c,d,e}
(iii)

{d,b}
(iv)

{c,a,b}
(v)

{a,b,e}

Question 56

56.

In the given figure, which of the following are true?

a)	∠A + ∠OBC + ∠OCB = 2 ∠A
b)	∠A + ∠BOC = 180°
c)	∠A + ∠OCB = 90°
d)	∠A + ∠OBC = 120°
e)	∠A + ∠OBC = 90°

(i)

{d,a,c}
(ii)

{c,e}
(iii)

{b,e}
(iv)

{b,e,c}
(v)

{a,c}

Question 57

57.

In the given figure, the bisectors of ∠E , ∠F & ∠G of △EFG meet the circumcircle at H , I & J. If ∠E = 43°, find ∠H

(i)

78.5°
(ii)

68.5°
(iii)

98.5°
(iv)

73.5°
(v)

83.5°

Question 58

58.

In the given figure, O is the centre of the circle. Given ∠HKJ = 60.5° & ∠HOI = 60°, find ∠IOJ

(i)

66°
(ii)

76°
(iii)

71°
(iv)

61°
(v)

91°

Question 59

59.

In the given figure, chords DF & EG meet at H. Given x = 116° and y = 38°, find ∠EDF

(i)

108°
(ii)

88°
(iii)

93°
(iv)

78°
(v)

83°

Question 60

60.

In the given figure, O is the centre of the circle. Given ∠FJI = 67.5°, ∠HOI = 34° and ∠FOG = 45°, find ∠GOH

(i)

86°
(ii)

61°
(iii)

66°
(iv)

71°
(v)

56°

Assignment Key