EduSahara™ Worksheet

Question 1

1.

(i)

131°
(ii)

121°
(iii)

146°
(iv)

116°
(v)

126°

Question 2

2.

O is the centre of the circle. If ∠DOF = 81°, find ∠C

(i)

55.5°
(ii)

40.5°
(iii)

50.5°
(iv)

70.5°
(v)

45.5°

Question 3

3.

O is the centre of the circle. If ∠COB = 124° and ∠DOB = 112°, find ∠CBD

(i)

67°
(ii)

62°
(iii)

72°
(iv)

77°
(v)

92°

Question 4

4.

Find the missing angle in the following figure?

(i)

25°
(ii)

55°
(iii)

30°
(iv)

40°
(v)

35°

Question 5

5.

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

(i)

90°
(ii)

60°
(iii)

65°
(iv)

75°
(v)

70°

Question 6

6.

O is the centre of the circle and OJ = IJ. Find ∠JOH

(i)

120°
(ii)

135°
(iii)

125°
(iv)

130°
(v)

150°

Question 7

7.

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

(i)

255°
(ii)

270°
(iii)

250°
(iv)

240°
(v)

245°

Question 8

8.

(i)

133°
(ii)

128°
(iii)

138°
(iv)

158°
(v)

143°

Question 9

9.

O is the centre of the circle. If ∠DFE = 41° and ∠FDG = 31°, find x°, y°

(i)

49°, 59°
(ii)

49°, 49°
(iii)

69°, 59°
(iv)

89°, 69°
(v)

59°, 49°

Question 10

10.

O is the centre of the circle. If ∠AOB = 65°, find the angle ∠C

(i)

32.5°
(ii)

62.5°
(iii)

42.5°
(iv)

37.5°
(v)

47.5°

Question 11

11.

Two circles touch internally. J is the centre of the bigger circle and lies on the smaller circle. If ∠GHI = 69°, find ∠G

(i)

51°
(ii)

21°
(iii)

31°
(iv)

26°
(v)

36°

Question 12

12.

△ABC is inscribed in a circle with centre O. If ∠AOB = 147° and ∠BOC = 154°, find ∠CAB

(i)

77°
(ii)

107°
(iii)

87°
(iv)

82°
(v)

92°

Question 13

13.

△GHI is inscribed in a circle with centre O. If ∠GOH = 134° and ∠HOI = 145°, find ∠GHI

(i)

40.5°
(ii)

55.5°
(iii)

45.5°
(iv)

70.5°
(v)

50.5°

Question 14

14.

△LMN is inscribed in a circle with centre O. If ∠LOM = 124° and ∠MON = 159°, find ∠MNL

(i)

62°
(ii)

67°
(iii)

77°
(iv)

72°
(v)

92°

Question 15

15.

O is the centre of the circle. If ∠ABC = 121.5°, find ∠COD

(i)

78°
(ii)

73°
(iii)

93°
(iv)

63°
(v)

68°

Question 16

16.

In the given figure, O is the centre of the circle. If ∠ADB = 53° and ∠OAD = 30°, find ∠CBD

(i)

150°
(ii)

135°
(iii)

125°
(iv)

130°
(v)

120°

Question 17

17.

In the given figure, O is the centre of the circle and FG is a diameter. If ∠GOI = 46°, find ∠FHI

(i)

67°
(ii)

97°
(iii)

82°
(iv)

77°
(v)

72°

Question 18

18.

In the given figure, O is the centre of the circle and HJ is a diameter. If ∠IGH = 65°, find ∠IHJ

(i)

35°
(ii)

25°
(iii)

40°
(iv)

55°
(v)

30°

Question 19

19.

In the given figure, O is the centre of the circle and BD is a diameter. If ∠AOD = 113° and ∠ODC = 62°, find ∠BCA + ∠CBD

(i)

91.5°
(ii)

71.5°
(iii)

61.5°
(iv)

76.5°
(v)

66.5°

Question 20

20.

In the given figure, O is the centre of the circle and BD is a diameter. If ∠ACB = 23° and ∠BAC = 64°, find ∠DBC + ∠ACD

(i)

93°
(ii)

98°
(iii)

108°
(iv)

103°
(v)

123°

Question 21

21.

In the given figure, O is the centre of the circle. If ∠JIK = 59° and ∠IKL = 13°, find ∠KML

(i)

138°
(ii)

113°
(iii)

118°
(iv)

123°
(v)

108°

Question 22

22.

O is the centre of the circle. If Arc EG = 2 Arc GH and ∠EOG = 90°, find ∠EHG

(i)

60°
(ii)

75°
(iii)

45°
(iv)

50°
(v)

55°

Question 23

23.

O is the centre of the circle. If Arc FH = 2 Arc HI and ∠FOH = 93°, find ∠IFH

(i)

28.2°
(ii)

38.2°
(iii)

33.2°
(iv)

53.2°
(v)

23.2°

Question 24

24.

O is the centre of the circle. If Arc HJ = 2 Arc JK and ∠HOJ = 82°, find ∠HIJ

(i)

139°
(ii)

169°
(iii)

154°
(iv)

144°
(v)

149°

Question 25

25.

In the given figure, a pentagon is inscribed in a circle with centre O. Given IJ = JK = KL and ∠IJK = 110°. Find ∠KOL

(i)

100°
(ii)

85°
(iii)

75°
(iv)

70°
(v)

80°

Question 26

26.

In the given figure, GH is a side of regular 8-sided polygon and GI is a side of regular 6-sided polygon inscribed in a circle with centre O. Find ∠GOH

(i)

45°
(ii)

55°
(iii)

75°
(iv)

50°
(v)

60°

Question 27

27.

In the given figure, DE is a side of regular 9-sided polygon and DF is a side of regular 6-sided polygon inscribed in a circle with centre O. Find ∠DFE

(i)

30°
(ii)

50°
(iii)

25°
(iv)

20°
(v)

35°

Question 28

28.

In the given figure, GH is a side of regular 6-sided polygon and GI is a side of regular 10-sided polygon inscribed in a circle with centre O. Find ∠GHI

(i)

18°
(ii)

28°
(iii)

33°
(iv)

23°
(v)

48°

Question 29

29.

In the given figure, O is the centre of the circle, and OE ⟂ AB. If ∠ABC = 37.5°, find ∠AOC

(i)

80°
(ii)

105°
(iii)

75°
(iv)

85°
(v)

90°

Question 30

30.

In the given figure, O is the centre of the circle, and OJ ⟂ FG. If ∠FGH = 34.5°, find ∠OIH

(i)

65.5°
(ii)

85.5°
(iii)

60.5°
(iv)

70.5°
(v)

55.5°

Question 31

31.

In the given figure, O is the centre of the circle. If ∠GEF = 59.23° and ∠EFG = 78.96°, find the angle ∠EHF

(i)

71.81°
(ii)

56.81°
(iii)

41.81°
(iv)

46.81°
(v)

51.81°

Question 32

32.

Which of the following statements are true?

a)	The farther the chord is from the centre, the larger the angle it subtends at the centre.
b)	Equal length chords subtend equal angles at the centre of the circle.
c)	Equal length chords are equidistant from the centre of the circle.
d)	No two chords bisects each other.
e)	The longest chord of the circle passes through the centre of the circle.

(i)

{a,d,e}
(ii)

{a,b,c}
(iii)

{d,c}
(iv)

{b,c,e}
(v)

{a,b}

Question 33

33.

Which of the following statements are true?

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

(i)

{b,c,a}
(ii)

{d,c}
(iii)

{a,c}
(iv)

{b,a}
(v)

{b,d,a}

Question 34

34.

The point of intersection of the angular bisectors of a triangle is

(i)

circumcentre
(ii)

orthocentre
(iii)

centroid
(iv)

excentre
(v)

incentre

Question 35

35.

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

(i)

2x°
(ii)

4x°
(iii)

x°

2
(iv)

x°

Question 36

36.

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

(i)

quadrant
(ii)

semi-circle
(iii)

minor segment
(iv)

major arc
(v)

minor arc

Question 37

37.

An arc subtends 118° in its alternate segment. The arc is

(i)

semi-circle
(ii)

minor arc
(iii)

major segment
(iv)

major arc
(v)

quadrant

Question 38

38.

An arc subtends 67° in its alternate segment. The arc is

(i)

major arc
(ii)

quadrant
(iii)

minor arc
(iv)

minor segment
(v)

major segment

Question 39

39.

An arc subtends 39° in its alternate segment. Its corresponding major arc subtends what angle in its (major arc) alternate segment?

(i)

141°
(ii)

146°
(iii)

171°
(iv)

156°
(v)

151°

Question 40

40.

An arc subtends 53° in its alternate segment. The angle made by its corresponding major arc at the centre is

(i)

259°
(ii)

269°
(iii)

264°
(iv)

254°
(v)

284°

Question 41

41.

The angle subtended by the semicircle at the centre is

(i)

180°
(ii)

195°
(iii)

185°
(iv)

190°
(v)

210°

Question 42

42.

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

(i)

95°
(ii)

90°
(iii)

105°
(iv)

100°
(v)

120°

Question 43

43.

Angle subtended by the major arc at the centre is

(i)

reflex angle
(ii)

right angle
(iii)

zero angle
(iv)

obtuse angle
(v)

straight angle

Question 44

44.

Angle subtended in the major segment is

(i)

straight angle
(ii)

acute angle
(iii)

right angle
(iv)

obtuse angle
(v)

reflex angle

Question 45

45.

If the radius of the circumcircle is half the length of a side of the triangle, then the triangle is

(i)

right angle triangle
(ii)

acute angled triangle
(iii)

equilateral triangle
(iv)

obtuse angled triangle

Question 46

46.

In the given figure, AB & CD are diameters of the circle. If ∠ABC = 67° find, ∠BOC

(i)

61°
(ii)

56°
(iii)

51°
(iv)

46°
(v)

76°

Question 47

47.

In the given figure, AB & CD are diameters of the circle. If ∠ADC = 46°, find ∠OCB

(i)

61°
(ii)

76°
(iii)

51°
(iv)

46°
(v)

56°

Question 48

48.

In the given figure IK & JK are equal length chords of the circle. Find ∠KIJ

(i)

55°
(ii)

50°
(iii)

75°
(iv)

45°
(v)

60°

Question 49

49.

In the given figure, AB is a diameter of the circle with centre O. If ∠BAC = 23.54° and BC = BD, find ∠DCA

(i)

96.46°
(ii)

66.46°
(iii)

71.46°
(iv)

76.46°
(v)

81.46°

Question 50

50.

In the given figure, O is the centre of the circle. If ∠OAC = 31.5°, find ∠B

(i)

131.5°
(ii)

136.5°
(iii)

126.5°
(iv)

121.5°
(v)

151.5°

Question 51

51.

In the given figure, O is the centre of the circle. If ∠HIJ = 126°, find ∠OHJ

(i)

51°
(ii)

41°
(iii)

66°
(iv)

46°
(v)

36°

Question 52

52.

In the given figure, O is the centre of the circle and IK is the tangent at J. If ∠JKL = 48°,∠KJL = 30°, find ∠MJL

(i)

82°
(ii)

72°
(iii)

87°
(iv)

77°
(v)

102°

Question 53

53.

O is the centre of the circle. If ∠IJH = 31.5°, find the angle ∠OIH

(i)

88.5°
(ii)

68.5°
(iii)

63.5°
(iv)

58.5°
(v)

73.5°

Question 54

54.

GH is the perpendicular bisector of side EF of △DEF. Given ∠DEF = 65° and ∠GDF = 42° , find ∠DFE

(i)

41°
(ii)

36°
(iii)

46°
(iv)

31°
(v)

61°

Question 55

55.

In the given figure, △KHI is a scalene triangle. JH bisects ∠KHI. Similarly IJ bisects ∠HIK. Given ∠IKH = 134°, find ∠IJH

(i)

172°
(ii)

162°
(iii)

157°
(iv)

187°
(v)

167°

Question 56

56.

In the given figure, △HDE is a scalene triangle. FD & GD trisect ∠HDE. Similarly EF & EG trisect ∠DEH. Given ∠EHD = 60°, find ∠EFD

(i)

150°
(ii)

140°
(iii)

155°
(iv)

170°
(v)

145°

Question 57

57.

In the given figure, △LHI is a scalene triangle. JH & KH trisect ∠LHI. Similarly IJ & IK trisect ∠HIL. Given ∠ILH = 63°, find ∠IKH

(i)

107°
(ii)

117°
(iii)

102°
(iv)

132°
(v)

112°

Question 58

58.

In the given figure, EF , FG , GH and HI are chords and EH , FI are diameters passing through the centre O. If ∠EOF = 64°. Find ∠FGH

(i)

122°
(ii)

127°
(iii)

152°
(iv)

132°
(v)

137°

Question 59

59.

In the given figure, JKLMNO is a regular hexagon inscribed in a circle with centre O. Which of the following are true?

a)	∠JOO = 60°
b)	∠KNL = 30°
c)	∠OML = 90°
d)	∠KOM = 120°
e)	∠JLK = 60°

(i)

{e,a}
(ii)

{a,b,c,d}
(iii)

{e,c}
(iv)

{e,b}
(v)

{e,d,a}

Question 60

60.

In the given figure, CDEFG is a regular pentagon . Find ∠CGE

(i)

77°
(ii)

102°
(iii)

82°
(iv)

72°
(v)

87°

Question 61

61.

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 in the major segment is obtuse.
c)	Angle subtended by the major arc at the centre is acute.
d)	Angle subtended by the major arc in its alternate segment is obtuse.
e)	The angle subtended in a semicircle is a right angle.

(i)

{b,a}
(ii)

{c,d}
(iii)

{a,d,e}
(iv)

{b,a,d}
(v)

{b,c,e}

Question 62

62.

In triangle IJK, if a circle is drawn with JK as diameter and if it passes through I it is a

(i)

equilateral triangle
(ii)

obtuse angled triangle
(iii)

acute angled triangle
(iv)

right angle triangle

Question 63

63.

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

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

(i)

{e,a,b}
(ii)

{d,c,b}
(iii)

{b,c}
(iv)

{d,c}
(v)

{a,b}

Question 64

64.

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)

83.5°
(ii)

98.5°
(iii)

73.5°
(iv)

68.5°
(v)

78.5°

Question 65

65.

In the given figure, which of the following angle pairs are equal?

(i)

{(i,j),(e,h),(c,f),(d,g)}
(ii)

{(h,c),(j,f),(i,d),(e,g)}
(iii)

{(c,h),(d,g),(e,j),(f,i)}
(iv)

{(g,h),(j,f),(d,i),(e,c)}
(v)

{(i,d),(f,j),(g,e),(h,c)}

Assignment Key