EduSahara™ Worksheet

Question 1

1.

(i)

128.5°
(ii)

143.5°
(iii)

158.5°
(iv)

133.5°
(v)

138.5°

Question 2

2.

O is the centre of the circle. If ∠KOM = 83°, find ∠J

(i)

56.5°
(ii)

51.5°
(iii)

71.5°
(iv)

46.5°
(v)

41.5°

Question 3

3.

O is the centre of the circle. If ∠KOJ = 113° and ∠LOJ = 77°, find ∠KJL

(i)

85°
(ii)

115°
(iii)

100°
(iv)

95°
(v)

90°

Question 4

4.

Find the missing angle in the following figure?

(i)

68°
(ii)

43°
(iii)

48°
(iv)

53°
(v)

38°

Question 5

5.

O is the centre of the circle and OG = FG. Find ∠FOG

(i)

70°
(ii)

90°
(iii)

60°
(iv)

75°
(v)

65°

Question 6

6.

O is the centre of the circle and OL = KL. Find ∠LOJ

(i)

150°
(ii)

135°
(iii)

120°
(iv)

125°
(v)

130°

Question 7

7.

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

(i)

255°
(ii)

270°
(iii)

240°
(iv)

245°
(v)

250°

Question 8

8.

(i)

82°
(ii)

52°
(iii)

57°
(iv)

67°
(v)

62°

Question 9

9.

O is the centre of the circle. If ∠GIH = 53° and ∠IGJ = 55°, find u°, v°

(i)

25°, 37°
(ii)

45°, 47°
(iii)

35°, 37°
(iv)

65°, 57°
(v)

37°, 35°

Question 10

10.

O is the centre of the circle. If ∠HOI = 130°, find the angle ∠J

(i)

95°
(ii)

75°
(iii)

70°
(iv)

80°
(v)

65°

Question 11

11.

Two circles touch internally. H is the centre of the bigger circle and lies on the smaller circle. If ∠EFG = 37°, find ∠E

(i)

68°
(ii)

58°
(iii)

83°
(iv)

63°
(v)

53°

Question 12

12.

△BCD is inscribed in a circle with centre O. If ∠BOC = 104° and ∠COD = 116°, find ∠DBC

(i)

73°
(ii)

68°
(iii)

58°
(iv)

63°
(v)

88°

Question 13

13.

△EFG is inscribed in a circle with centre O. If ∠EOF = 110° and ∠FOG = 132°, find ∠EFG

(i)

89°
(ii)

69°
(iii)

74°
(iv)

64°
(v)

59°

Question 14

14.

△JKL is inscribed in a circle with centre O. If ∠JOK = 147° and ∠KOL = 150°, find ∠KLJ

(i)

83.5°
(ii)

78.5°
(iii)

88.5°
(iv)

73.5°
(v)

103.5°

Question 15

15.

O is the centre of the circle. If ∠ABC = 116°, find ∠COD

(i)

67°
(ii)

82°
(iii)

57°
(iv)

52°
(v)

62°

Question 16

16.

In the given figure, O is the centre of the circle. If ∠FIG = 42° and ∠OFI = 34°, find ∠HGI

(i)

139°
(ii)

124°
(iii)

129°
(iv)

134°
(v)

154°

Question 17

17.

In the given figure, O is the centre of the circle and DE is a diameter. If ∠EOG = 91°, find ∠DFG

(i)

54.5°
(ii)

49.5°
(iii)

44.5°
(iv)

74.5°
(v)

59.5°

Question 18

18.

In the given figure, O is the centre of the circle and IK is a diameter. If ∠JHI = 60°, find ∠JIK

(i)

30°
(ii)

35°
(iii)

40°
(iv)

60°
(v)

45°

Question 19

19.

In the given figure, O is the centre of the circle and HJ is a diameter. If ∠GOJ = 101° and ∠OJI = 62°, find ∠HIG + ∠IHJ

(i)

97.5°
(ii)

77.5°
(iii)

82.5°
(iv)

67.5°
(v)

72.5°

Question 20

20.

In the given figure, O is the centre of the circle and BD is a diameter. If ∠ACB = 30° and ∠BAC = 62°, find ∠DBC + ∠ACD

(i)

88°
(ii)

93°
(iii)

98°
(iv)

118°
(v)

103°

Question 21

21.

In the given figure, O is the centre of the circle. If ∠KJL = 59° and ∠JLM = 27°, find ∠LNM

(i)

109°
(ii)

94°
(iii)

99°
(iv)

104°
(v)

124°

Question 22

22.

O is the centre of the circle. If Arc JL = 2 Arc LM and ∠JOL = 70°, find ∠JML

(i)

40°
(ii)

35°
(iii)

45°
(iv)

50°
(v)

65°

Question 23

23.

O is the centre of the circle. If Arc HJ = 2 Arc JK and ∠HOJ = 71°, find ∠KHJ

(i)

17.8°
(ii)

22.8°
(iii)

32.8°
(iv)

27.8°
(v)

47.8°

Question 24

24.

O is the centre of the circle. If Arc HJ = 2 Arc JK and ∠HOJ = 84°, find ∠HIJ

(i)

143°
(ii)

153°
(iii)

138°
(iv)

168°
(v)

148°

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)

80°
(ii)

85°
(iii)

75°
(iv)

100°
(v)

70°

Question 26

26.

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

(i)

72°
(ii)

87°
(iii)

77°
(iv)

82°
(v)

102°

Question 27

27.

In the given figure, BC is a side of regular 5-sided polygon and BD is a side of regular 6-sided polygon inscribed in a circle with centre O. Find ∠BDC

(i)

41°
(ii)

36°
(iii)

46°
(iv)

66°
(v)

51°

Question 28

28.

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

(i)

66°
(ii)

51°
(iii)

41°
(iv)

36°
(v)

46°

Question 29

29.

In the given figure, O is the centre of the circle, and OK ⟂ GH. If ∠GHI = 45.5°, find ∠GOI

(i)

96°
(ii)

101°
(iii)

106°
(iv)

91°
(v)

121°

Question 30

30.

In the given figure, O is the centre of the circle, and OG ⟂ CD. If ∠CDE = 36.5°, find ∠OFE

(i)

58.5°
(ii)

53.5°
(iii)

63.5°
(iv)

83.5°
(v)

68.5°

Question 31

31.

In the given figure, O is the centre of the circle. If ∠CAB = 54.47° and ∠ABC = 75.86°, find the angle ∠ADB

(i)

59.67°
(ii)

49.67°
(iii)

79.67°
(iv)

54.67°
(v)

64.67°

Question 32

32.

Which of the following statements are true?

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

(i)

{a,c,e}
(ii)

{d,c}
(iii)

{b,a}
(iv)

{b,d,e}
(v)

{b,a,c}

Question 33

33.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{a,d,b}
(iii)

{c,d}
(iv)

{a,c,b}
(v)

{b,d}

Question 34

34.

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

(i)

circumcentre
(ii)

centroid
(iii)

incentre
(iv)

excentre
(v)

orthocentre

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)

x°

2
(ii)

x°
(iii)

4x°
(iv)

2x°

Question 36

36.

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

(i)

major segment
(ii)

minor segment
(iii)

semi-circle
(iv)

major arc
(v)

quadrant

Question 37

37.

An arc subtends 143° in its alternate segment. The arc is

(i)

major segment
(ii)

major arc
(iii)

quadrant
(iv)

semi-circle
(v)

minor segment

Question 38

38.

An arc subtends 61° in its alternate segment. The arc is

(i)

minor arc
(ii)

semi-circle
(iii)

quadrant
(iv)

major arc
(v)

major segment

Question 39

39.

An arc subtends 61° in its alternate segment. Its corresponding major arc subtends what angle in its (major arc) alternate segment?

(i)

149°
(ii)

134°
(iii)

124°
(iv)

129°
(v)

119°

Question 40

40.

An arc subtends 46° in its alternate segment. The angle made by its corresponding major arc at the centre is

(i)

278°
(ii)

273°
(iii)

268°
(iv)

298°
(v)

283°

Question 41

41.

The angle subtended by the semicircle at the centre is

(i)

180°
(ii)

195°
(iii)

185°
(iv)

210°
(v)

190°

Question 42

42.

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

(i)

120°
(ii)

105°
(iii)

100°
(iv)

95°
(v)

90°

Question 43

43.

Angle subtended by the major arc at the centre is

(i)

acute angle
(ii)

reflex angle
(iii)

right angle
(iv)

obtuse angle
(v)

zero angle

Question 44

44.

Angle subtended in the major segment is

(i)

straight angle
(ii)

complete angle
(iii)

right angle
(iv)

zero angle
(v)

acute 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)

obtuse angled triangle
(ii)

acute angled triangle
(iii)

equilateral triangle
(iv)

right angle triangle

Question 46

46.

In the given figure, FG & HI are diameters of the circle. If ∠FGH = 65° find, ∠GOH

(i)

80°
(ii)

60°
(iii)

50°
(iv)

65°
(v)

55°

Question 47

47.

In the given figure, GH & IJ are diameters of the circle. If ∠GJI = 25°, find ∠OIH

(i)

35°
(ii)

25°
(iii)

40°
(iv)

55°
(v)

30°

Question 48

48.

In the given figure AC & BC are equal length chords of the circle. Find ∠CAB

(i)

75°
(ii)

55°
(iii)

45°
(iv)

50°
(v)

60°

Question 49

49.

In the given figure, EF is a diameter of the circle with centre O. If ∠FEG = 25.6° and FG = FH, find ∠HGE

(i)

64.4°
(ii)

69.4°
(iii)

79.4°
(iv)

94.4°
(v)

74.4°

Question 50

50.

In the given figure, O is the centre of the circle. If ∠OEG = 38.5°, find ∠F

(i)

138.5°
(ii)

158.5°
(iii)

133.5°
(iv)

128.5°
(v)

143.5°

Question 51

51.

In the given figure, O is the centre of the circle. If ∠FGH = 117°, find ∠OFH

(i)

32°
(ii)

57°
(iii)

42°
(iv)

27°
(v)

37°

Question 52

52.

In the given figure, O is the centre of the circle and BD is the tangent at C. If ∠CDE = 35°,∠DCE = 40°, find ∠FCE

(i)

75°
(ii)

95°
(iii)

80°
(iv)

70°
(v)

65°

Question 53

53.

O is the centre of the circle. If ∠HIG = 45.5°, find the angle ∠OHG

(i)

59.5°
(ii)

54.5°
(iii)

49.5°
(iv)

44.5°
(v)

74.5°

Question 54

54.

KL is the perpendicular bisector of side IJ of △HIJ. Given ∠HIJ = 47° and ∠KHJ = 50° , find ∠HJI

(i)

48°
(ii)

38°
(iii)

33°
(iv)

63°
(v)

43°

Question 55

55.

In the given figure, △HEF is a scalene triangle. GE bisects ∠HEF. Similarly FG bisects ∠EFH. Given ∠FHE = 98°, find ∠FGE

(i)

139°
(ii)

169°
(iii)

144°
(iv)

149°
(v)

154°

Question 56

56.

In the given figure, △HDE is a scalene triangle. FD & GD trisect ∠HDE. Similarly EF & EG trisect ∠DEH. Given ∠EHD = 78°, find ∠EFD

(i)

161°
(ii)

146°
(iii)

176°
(iv)

156°
(v)

151°

Question 57

57.

In the given figure, △MIJ is a scalene triangle. KI & LI trisect ∠MIJ. Similarly JK & JL trisect ∠IJM. Given ∠JMI = 99°, find ∠JLI

(i)

156°
(ii)

136°
(iii)

131°
(iv)

141°
(v)

126°

Question 58

58.

In the given figure, DE , EF , FG and GH are chords and DG , EH are diameters passing through the centre O. If ∠DOE = 60°. Find ∠EFG

(i)

130°
(ii)

135°
(iii)

120°
(iv)

125°
(v)

150°

Question 59

59.

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

a)	∠ACB = 60°
b)	∠AOF = 60°
c)	∠FDC = 90°
d)	∠BOD = 120°
e)	∠BEC = 30°

(i)

{b,c,d,e}
(ii)

{a,b}
(iii)

{a,c}
(iv)

{a,e,b}
(v)

{a,d}

Question 60

60.

In the given figure, EFGHI is a regular pentagon . Find ∠EIG

(i)

72°
(ii)

102°
(iii)

77°
(iv)

87°
(v)

82°

Question 61

61.

Which of the following statements are true?

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

(i)

{c,a}
(ii)

{d,b}
(iii)

{c,d,e}
(iv)

{c,a,b}
(v)

{a,b,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)

obtuse angled triangle
(ii)

equilateral triangle
(iii)

right angle triangle
(iv)

acute angled triangle

Question 63

63.

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

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

(i)

{b,d,c}
(ii)

{e,a,c}
(iii)

{a,c}
(iv)

{b,d}
(v)

{c,d}

Question 64

64.

In the given figure, the bisectors of ∠C , ∠D & ∠E of △CDE meet the circumcircle at F , G & H. If ∠C = 60°, find ∠F

(i)

75°
(ii)

70°
(iii)

65°
(iv)

60°
(v)

90°

Question 65

65.

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

(i)

{(m,r),(n,q),(o,t),(p,s)}
(ii)

{(m,o),(s,q),(r,n),(p,t)}
(iii)

{(m,o),(q,n),(p,r),(t,s)}
(iv)

{(o,s),(m,t),(n,r),(p,q)}
(v)

{(q,p),(o,s),(t,n),(m,r)}

Assignment Key