EduSahara™ Worksheet

Question 1

1.

Two angles of a triangle measure 59° and 59° respectively. Find the measure of the third angle of the triangle

(i)

62°
(ii)

60°
(iii)

63°
(iv)

61°
(v)

64°

Question 2

2.

The angles of a triangle ABC are in the ratio 6 : 13 : 26. Find the measure of each angle of the triangle

(i)

A

=

22°

,

B

=

54°

,

C

=

104°
(ii)

A

=

22°

,

B

=

52°

,

C

=

106°
(iii)

A

=

26°

,

B

=

52°

,

C

=

102°
(iv)

A

=

24°

,

B

=

50°

,

C

=

106°
(v)

A

=

24°

,

B

=

52°

,

C

=

104°

Question 3

3.

Find the unknown angle from the following figure

(i)

x

=

38.42°
(ii)

x

=

39.42°
(iii)

x

=

37.42°
(iv)

x

=

40.42°
(v)

x

=

36.42°

Question 4

4.

In the given figure, △IJK in which side JK has been produced to L. If ∠KIJ = x° , ∠IJK = (7/15a)° , ∠JKI = (1/3a)° and ∠IKL = (13/15a)°, find the values of a and x.

(i)

a

=

151°

,

x

=

61°
(ii)

a

=

149°

,

x

=

59°
(iii)

a

=

152°

,

x

=

62°
(iv)

a

=

148°

,

x

=

58°
(v)

a

=

150°

,

x

=

60°

Question 5

5.

Find the angles of the triangle

(i)

A

=

40°

,

B

=

20°

,

C

=

120°
(ii)

A

=

38°

,

B

=

22°

,

C

=

120°
(iii)

A

=

42°

,

B

=

20°

,

C

=

118°
(iv)

A

=

40°

,

B

=

18°

,

C

=

122°
(v)

A

=

38°

,

B

=

20°

,

C

=

122°

Question 6

6.

Calculate the value of x in the following figure

(i)

x

=

40.04°
(ii)

x

=

39.04°
(iii)

x

=

41.04°
(iv)

x

=

43.04°
(v)

x

=

42.04°

Question 7

7.

Calculate the value of x in the following figure

(i)

x

=

56.93°
(ii)

x

=

57.93°
(iii)

x

=

58.93°
(iv)

x

=

54.93°
(v)

x

=

55.93°

Question 8

8.

Find the unknown marked angle in the following figure

(i)

x

=

68.2°
(ii)

x

=

70.2°
(iii)

x

=

69.2°
(iv)

x

=

72.2°
(v)

x

=

71.2°

Question 9

9.

Find the unknown angles in the following figure

(i)

C

=

54°

,

D

=

54°
(ii)

C

=

50°

,

D

=

50°
(iii)

C

=

51°

,

D

=

51°
(iv)

C

=

53°

,

D

=

53°
(v)

C

=

52°

,

D

=

52°

Question 10

10.

In the following figure, one side of a triangle has been produced. Find all the angles of the triangle

(i)

I

=

20°

,

J

=

50°

,

K

=

110°
(ii)

I

=

20°

,

J

=

48°

,

K

=

112°
(iii)

I

=

18°

,

J

=

52°

,

K

=

110°
(iv)

I

=

18°

,

J

=

50°

,

K

=

112°
(v)

I

=

22°

,

J

=

50°

,

K

=

108°

Question 11

11.

In the following figure, one side of a triangle has been produced. Find all the angles of the triangle.

(i)

C

=

57°

,

D

=

25°

,

E

=

98°
(ii)

C

=

55°

,

D

=

23°

,

E

=

102°
(iii)

C

=

53°

,

D

=

25°

,

E

=

102°
(iv)

C

=

55°

,

D

=

25°

,

E

=

100°
(v)

C

=

53°

,

D

=

27°

,

E

=

100°

Question 12

12.

In the following figure, two sides of a triangle have been produced. Find all the angles of the triangle.

(i)

x

=

18°

,

y

=

50°

,

z

=

112°
(ii)

x

=

20°

,

y

=

48°

,

z

=

112°
(iii)

x

=

18°

,

y

=

52°

,

z

=

110°
(iv)

x

=

20°

,

y

=

50°

,

z

=

110°
(v)

x

=

22°

,

y

=

50°

,

z

=

108°

Question 13

13.

In the following figure, one side of a triangle has been produced. Find the values of x and y.

(i)

x

=

43°

,

y

=

97°
(ii)

x

=

47°

,

y

=

101°
(iii)

x

=

45°

,

y

=

99°
(iv)

x

=

46°

,

y

=

100°
(v)

x

=

44°

,

y

=

98°

Question 14

14.

Calculate the value of the lettered angle in the following figure

(i)

x

=

59.17°
(ii)

x

=

61.17°
(iii)

x

=

60.17°
(iv)

x

=

62.17°
(v)

x

=

58.17°

Question 15

15.

Calculate the value of the lettered angle in the following figure

(i)

x

=

20.91°
(ii)

x

=

17.91°
(iii)

x

=

19.91°
(iv)

x

=

18.91°
(v)

x

=

21.91°

Question 16

16.

In the given triangle, ∠I = 69.74°. Find the measure of ∠J and ∠K

(i)

∠J = ∠K = 53.13°
(ii)

∠J = ∠K = 54.13°
(iii)

∠J = ∠K = 57.13°
(iv)

∠J = ∠K = 55.13°
(v)

∠J = ∠K = 56.13°

Question 17

17.

Find the unknown angle in the following figure

(i)

x

=

46.95°
(ii)

x

=

47.95°
(iii)

x

=

48.95°
(iv)

x

=

45.95°
(v)

x

=

44.95°

Question 18

18.

Find the unknown angle in the following figure

(i)

x

=

43°
(ii)

x

=

47°
(iii)

x

=

45°
(iv)

x

=

44°
(v)

x

=

46°

Question 19

19.

Find the unknown angle in the following figure

(i)

x

=

135°
(ii)

x

=

134°
(iii)

x

=

136°
(iv)

x

=

137°
(v)

x

=

133°

Question 20

20.

In △FGH, if ∠F = 53° and ∠G = 66°, find the measure of ∠H

(i)

H

=

60°
(ii)

H

=

63°
(iii)

H

=

61°
(iv)

H

=

59°
(v)

H

=

62°

Question 21

21.

In △GHI, if ∠G = 70° and ∠H = ∠I, find the measure of each of the equal angles of the triangle

(i)

54°
(ii)

55°
(iii)

56°
(iv)

53°
(v)

57°

Question 22

22.

One angle of a triangle measures 36° and the other two angles are in the ratio 3 : 5. Find these angles.

(i)

B

=

56°

,

C

=

92°
(ii)

B

=

52°

,

C

=

88°
(iii)

B

=

54°

,

C

=

90°
(iv)

B

=

55°

,

C

=

91°
(v)

B

=

53°

,

C

=

89°

Question 23

23.

In a right-angled triangle, the two acute angles are in the ratio 2 : 1. Find these angles.

(i)

A

=

61°

,

C

=

31°
(ii)

A

=

58°

,

C

=

28°
(iii)

A

=

59°

,

C

=

29°
(iv)

A

=

62°

,

C

=

32°
(v)

A

=

60°

,

C

=

30°

Question 24

24.

One of the two equal angles of an isosceles triangle measures 38°. Find the measure of each angle of the triangle.

(i)

A

=

38°

,

B

=

36°

,

C

=

106°
(ii)

A

=

36°

,

B

=

40°

,

C

=

104°
(iii)

A

=

38°

,

B

=

38°

,

C

=

104°
(iv)

A

=

36°

,

B

=

38°

,

C

=

106°
(v)

A

=

40°

,

B

=

38°

,

C

=

102°

Question 25

25.

Find the measure of each of the two equal angles of an isosceles right-angled triangle.

(i)

46°
(ii)

43°
(iii)

47°
(iv)

45°
(v)

44°

Question 26

26.

If all the three angles of a triangle are of the same measure, find the measure of each of the angles.

(i)

58°
(ii)

59°
(iii)

62°
(iv)

61°
(v)

60°

Question 27

27.

In a right-angled triangle if one of the acute angles is 52°, find the measure of the other acute angle.

(i)

37°
(ii)

40°
(iii)

36°
(iv)

39°
(v)

38°

Question 28

28.

The vertical angle of an isosceles triangle is twice the sum of its base angles. Find each angle of the triangle.

(i)

A

=

120°

,

B

=

28°

,

C

=

32°
(ii)

A

=

122°

,

B

=

30°

,

C

=

28°
(iii)

A

=

120°

,

B

=

30°

,

C

=

30°
(iv)

A

=

118°

,

B

=

30°

,

C

=

32°
(v)

A

=

118°

,

B

=

32°

,

C

=

30°

Question 29

29.

In an isosceles triangle, each base angle is four times its vertical angle. Find each angle of the triangle.

(i)

A

=

22°

,

B

=

80°

,

C

=

78°
(ii)

A

=

18°

,

B

=

80°

,

C

=

82°
(iii)

A

=

20°

,

B

=

78°

,

C

=

82°
(iv)

A

=

20°

,

B

=

80°

,

C

=

80°
(v)

A

=

18°

,

B

=

82°

,

C

=

80°

Question 30

30.

The ratio between the base angle and the vertical angle of an isosceles triangle is 13 : 10. Find each angle of the triangle

(i)

A

=

50°

,

B

=

65°

,

C

=

65°
(ii)

A

=

52°

,

B

=

65°

,

C

=

63°
(iii)

A

=

50°

,

B

=

63°

,

C

=

67°
(iv)

A

=

48°

,

B

=

65°

,

C

=

67°
(v)

A

=

48°

,

B

=

67°

,

C

=

65°

Question 31

31.

In the given figure, find ∠KLJ

(i)

50°
(ii)

49°
(iii)

53°
(iv)

51°
(v)

52°

Question 32

32.

In the given figure, find ∠IGH

(i)

119°
(ii)

117°
(iii)

118°
(iv)

121°
(v)

120°

Question 33

33.

In the given figure, find ∠FGE

(i)

32°
(ii)

35°
(iii)

33°
(iv)

31°
(v)

34°

Question 34

34.

In the given figure, find ∠GKJ

(i)

148°
(ii)

147°
(iii)

145°
(iv)

146°
(v)

149°

Question 35

35.

In the given figure , if HE ⟂ FG and ∠EFH = 46.31°, find ∠HEF

(i)

44.69°
(ii)

41.69°
(iii)

45.69°
(iv)

43.69°
(v)

42.69°

Question 36

36.

In the given figure , if DA ⟂ BC and ∠ABD = 47.73°, find ∠CAD

(i)

26.61°
(ii)

28.61°
(iii)

29.61°
(iv)

27.61°
(v)

30.61°

Question 37

37.

In the given figure , if KH ⟂ IJ and ∠HIK = 47.2°, find ∠KJH

(i)

62.95°
(ii)

61.95°
(iii)

60.95°
(iv)

58.95°
(v)

59.95°

Question 38

38.

In below given figure, find ∠KNM

(i)

119.85°
(ii)

118.85°
(iii)

116.85°
(iv)

120.85°
(v)

117.85°

Question 39

39.

In below given figure, find ∠JGH

(i)

80.65°
(ii)

79.65°
(iii)

77.65°
(iv)

81.65°
(v)

78.65°

Question 40

40.

In below given figure, find ∠MKO

(i)

100.74°
(ii)

99.74°
(iii)

102.74°
(iv)

101.74°
(v)

98.74°

Question 41

41.

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

(i)

x

=

29.69°

,

y

=

52.99°
(ii)

x

=

30.69°

,

y

=

53.99°
(iii)

x

=

28.69°

,

y

=

51.99°
(iv)

x

=

31.69°

,

y

=

54.99°
(v)

x

=

27.69°

,

y

=

50.99°

Question 42

42.

Each of the two equal angles of an isosceles triangle is half the third angle. Find the angles of the triangle

(i)

X

=

43°

,

Y

=

92°

,

Z

=

45°
(ii)

X

=

43°

,

Y

=

90°

,

Z

=

47°
(iii)

X

=

45°

,

Y

=

88°

,

Z

=

47°
(iv)

X

=

47°

,

Y

=

90°

,

Z

=

43°
(v)

X

=

45°

,

Y

=

90°

,

Z

=

45°

Question 43

43.

(i)

122°
(ii)

121°
(iii)

118°
(iv)

119°
(v)

120°

Question 44

44.

In the given figure, △IJK is a triangle in which ∠J = 68.62° and ∠K = 55.29°.

If 'z' is the angle between the bisector of ∠J and ∠K, then find z.

(i)

119.04°
(ii)

118.04°
(iii)

120.04°
(iv)

116.04°
(v)

117.04°

Question 45

45.

In the given figure, ∠I = 54.08° and ∠J = 69.99°.

Side JK is produced to L, so that ∠JKI and ∠IKL form a linear pair.

(i)

x

=

29.96°

,

y

=

64.03°
(ii)

x

=

25.96°

,

y

=

60.03°
(iii)

x

=

27.96°

,

y

=

62.03°
(iv)

x

=

28.96°

,

y

=

63.03°
(v)

x

=

26.96°

,

y

=

61.03°

Question 46

46.

In the given figure, find the values of x and y

(i)

x

=

45.92°

,

y

=

51.57°
(ii)

x

=

41.92°

,

y

=

47.57°
(iii)

x

=

44.92°

,

y

=

50.57°
(iv)

x

=

43.92°

,

y

=

49.57°
(v)

x

=

42.92°

,

y

=

48.57°

Question 47

47.

In the given figure, △CDE in which ∠D = 65.29° and ∠E = 65.29°. CF and DE bisects each other. Find the value of z

(i)

z

=

51.42°
(ii)

z

=

49.42°
(iii)

z

=

47.42°
(iv)

z

=

50.42°
(v)

z

=

48.42°

Question 48

48.

In the given figure, QR ∥ ST, ∠DAR = 57° and AB = CA. Find the measure of x.

(i)

x

=

65°
(ii)

x

=

66°
(iii)

x

=

68°
(iv)

x

=

67°
(v)

x

=

64°

Question 49

49.

In the given figure, find the value of x.

(i)

x

=

23.5°
(ii)

x

=

24.5°
(iii)

x

=

27.5°
(iv)

x

=

26.5°
(v)

x

=

25.5°

Question 50

50.

In the given figure, EF ∥ GH and EG = GI. Find the values of x,y and z.

(i)

x

=

31°

,

y

=

74°

,

z

=

36°
(ii)

x

=

31°

,

y

=

72°

,

z

=

38°
(iii)

x

=

33°

,

y

=

72°

,

z

=

36°
(iv)

x

=

35°

,

y

=

72°

,

z

=

34°
(v)

x

=

33°

,

y

=

70°

,

z

=

38°

Question 51

51.

In the given figure, if GE = EH = FH. Find the value of x.

(i)

x

=

99.5°
(ii)

x

=

98.5°
(iii)

x

=

96.5°
(iv)

x

=

97.5°
(v)

x

=

95.5°

Question 52

52.

In the given figure, if DB = DE = EC, find the value of x

(i)

x

=

22°
(ii)

x

=

23°
(iii)

x

=

25°
(iv)

x

=

26°
(v)

x

=

24°

Question 53

53.

In the given figure, if HE = FH and EI = IG , find the value of x.

(i)

x

=

62°
(ii)

x

=

61°
(iii)

x

=

63°
(iv)

x

=

64°
(v)

x

=

60°

Question 54

54.

In the given figure, if DG = HD, find the values of x , y , z and t

(i)

x =56.7°, y =26.72°, z =23.73° , t =117.35°
(ii)

x =56.7°, y =26.72°, z =25.73° , t =119.35°
(iii)

x =56.7°, y =26.72°, z =24.73° , t =118.35°
(iv)

x =56.7°, y =24.72°, z =22.73° , t =118.35°
(v)

x =56.7°, y =28.72°, z =26.73° , t =118.35°

Question 55

55.

In the given figure, calculate the value of x.

(i)

x

=

25°
(ii)

x

=

23°
(iii)

x

=

21°
(iv)

x

=

22°
(v)

x

=

24°

Question 56

56.

In the given figure, calculate the value of x.

(i)

x

=

70.01°
(ii)

x

=

72.01°
(iii)

x

=

71.01°
(iv)

x

=

73.01°
(v)

x

=

69.01°

Question 57

57.

In the given figure, calculate the value of x.

(i)

x

=

69.62°
(ii)

x

=

71.62°
(iii)

x

=

70.62°
(iv)

x

=

67.62°
(v)

x

=

68.62°

Question 58

58.

Find the unknown marked angles in the following figure

(i)

x

=

112°

,

y

=

45°
(ii)

x

=

115°

,

y

=

48°
(iii)

x

=

113°

,

y

=

46°
(iv)

x

=

111°

,

y

=

44°
(v)

x

=

114°

,

y

=

47°

Question 59

59.

Find the unknown marked angles in the following figure

(i)

x

=

110°

,

y

=

110°
(ii)

x

=

114°

,

y

=

114°
(iii)

x

=

111°

,

y

=

111°
(iv)

x

=

113°

,

y

=

113°
(v)

x

=

112°

,

y

=

112°

Question 60

60.

In the given figure, calculate the value of x.

(i)

x

=

136°
(ii)

x

=

135°
(iii)

x

=

134°
(iv)

x

=

138°
(v)

x

=

137°

Question 61

61.

In the given figure, calculate the value of x.

(i)

x

=

22.5°
(ii)

x

=

20.5°
(iii)

x

=

24.5°
(iv)

x

=

21.5°
(v)

x

=

23.5°

Question 62

62.

Find the unknown marked angles in the following figure

(i)

x

=

97°

,

y

=

144°
(ii)

x

=

99°

,

y

=

146°
(iii)

x

=

98°

,

y

=

145°
(iv)

x

=

100°

,

y

=

147°
(v)

x

=

96°

,

y

=

143°

Question 63

63.

In the following figure FG ∥ IH, find the values of x and y.

(i)

x

=

39°

,

y

=

105°
(ii)

x

=

36°

,

y

=

102°
(iii)

x

=

37°

,

y

=

103°
(iv)

x

=

38°

,

y

=

104°
(v)

x

=

40°

,

y

=

106°

Question 64

64.

Find the unknown marked angles in the following figure

(i)

x

=

93°

,

y

=

118°
(ii)

x

=

91°

,

y

=

116°
(iii)

x

=

92°

,

y

=

117°
(iv)

x

=

94°

,

y

=

119°
(v)

x

=

90°

,

y

=

115°

Question 65

65.

In the given figure, it is given that KJ ∥ ML , ∠KML = 51° and ∠KJI = 101°. Find the value of x.

(i)

x

=

27°
(ii)

x

=

30°
(iii)

x

=

26°
(iv)

x

=

28°
(v)

x

=

29°

Question 66

66.

In the given figure, find the values of x ,y and z.

(i)

x

=

33°

,

y

=

39°

,

z

=

72°
(ii)

x

=

31°

,

y

=

41°

,

z

=

72°
(iii)

x

=

35°

,

y

=

39°

,

z

=

70°
(iv)

x

=

31°

,

y

=

39°

,

z

=

74°
(v)

x

=

33°

,

y

=

37°

,

z

=

74°

Question 67

67.

Find the value of x in the given figure.

(i)

x

=

29°
(ii)

x

=

32°
(iii)

x

=

28°
(iv)

x

=

31°
(v)

x

=

30°

Question 68

68.

In the given figure, find the values of x ,y and z.

(i)

x

=

82°

,

y

=

53°

,

z

=

78°
(ii)

x

=

82°

,

y

=

51°

,

z

=

80°
(iii)

x

=

84°

,

y

=

51°

,

z

=

78°
(iv)

x

=

84°

,

y

=

49°

,

z

=

80°
(v)

x

=

86°

,

y

=

51°

,

z

=

76°

Question 69

69.

In the given two equilateral triangles, find ∠C + ∠E + ∠G + ∠D + ∠F + ∠H .

(i)

360°
(ii)

361°
(iii)

358°
(iv)

362°
(v)

359°

Question 70

70.

In a right angled triangle, if one of the angles is 37.57°, find the third angle

(i)

67.43°
(ii)

82.43°
(iii)

52.43°
(iv)

62.43°
(v)

57.43°

Question 71

71.

In a right angled triangle, if one of the angles is 53.75°, find the third angle

(i)

36.25°
(ii)

51.25°
(iii)

66.25°
(iv)

41.25°
(v)

46.25°

Assignment Key