EduSahara™ Worksheet

Question 1

1.

Two angles of a triangle measure 68° and 53° respectively. Find the measure of the third angle of the triangle

(i)

61°
(ii)

57°
(iii)

58°
(iv)

60°
(v)

59°

Question 2

2.

The angles of a triangle ABC are in the ratio 4 : 3 : 5. Find the measure of each angle of the triangle

(i)

A

=

58°

,

B

=

45°

,

C

=

77°
(ii)

A

=

60°

,

B

=

43°

,

C

=

77°
(iii)

A

=

58°

,

B

=

47°

,

C

=

75°
(iv)

A

=

62°

,

B

=

45°

,

C

=

73°
(v)

A

=

60°

,

B

=

45°

,

C

=

75°

Question 3

3.

Find the unknown angle from the following figure

(i)

x

=

41.75°
(ii)

x

=

39.75°
(iii)

x

=

38.75°
(iv)

x

=

40.75°
(v)

x

=

37.75°

Question 4

4.

In the given figure, △BCD in which side CD has been produced to E. If ∠DBC = x° , ∠BCD = (3a)° , ∠CDB = (9a)° and ∠BDE = (9a)°, find the values of a and x.

(i)

a

=

12°

,

x

=

62°
(ii)

a

=

8°

,

x

=

58°
(iii)

a

=

10°

,

x

=

60°
(iv)

a

=

11°

,

x

=

61°
(v)

a

=

9°

,

x

=

59°

Question 5

5.

Find the angles of the triangle

(i)

J

=

34°

,

K

=

47°

,

L

=

99°
(ii)

J

=

34°

,

K

=

45°

,

L

=

101°
(iii)

J

=

36°

,

K

=

43°

,

L

=

101°
(iv)

J

=

38°

,

K

=

45°

,

L

=

97°
(v)

J

=

36°

,

K

=

45°

,

L

=

99°

Question 6

6.

Calculate the value of x in the following figure

(i)

x

=

85.24°
(ii)

x

=

82.24°
(iii)

x

=

83.24°
(iv)

x

=

86.24°
(v)

x

=

84.24°

Question 7

7.

Calculate the value of x in the following figure

(i)

x

=

51.06°
(ii)

x

=

50.06°
(iii)

x

=

52.06°
(iv)

x

=

49.06°
(v)

x

=

48.06°

Question 8

8.

Find the unknown marked angle in the following figure

(i)

x

=

57.25°
(ii)

x

=

59.25°
(iii)

x

=

56.25°
(iv)

x

=

58.25°
(v)

x

=

55.25°

Question 9

9.

Find the unknown angles in the following figure

(i)

J

=

56°

,

K

=

56°
(ii)

J

=

58°

,

K

=

58°
(iii)

J

=

57°

,

K

=

57°
(iv)

J

=

55°

,

K

=

55°
(v)

J

=

59°

,

K

=

59°

Question 10

10.

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

(i)

J

=

20°

,

K

=

60°

,

L

=

100°
(ii)

J

=

20°

,

K

=

58°

,

L

=

102°
(iii)

J

=

18°

,

K

=

60°

,

L

=

102°
(iv)

J

=

18°

,

K

=

62°

,

L

=

100°
(v)

J

=

22°

,

K

=

60°

,

L

=

98°

Question 11

11.

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

(i)

C

=

45°

,

D

=

28°

,

E

=

107°
(ii)

C

=

43°

,

D

=

32°

,

E

=

105°
(iii)

C

=

43°

,

D

=

30°

,

E

=

107°
(iv)

C

=

45°

,

D

=

30°

,

E

=

105°
(v)

C

=

47°

,

D

=

30°

,

E

=

103°

Question 12

12.

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

(i)

x

=

58°

,

y

=

47°

,

z

=

75°
(ii)

x

=

60°

,

y

=

43°

,

z

=

77°
(iii)

x

=

60°

,

y

=

45°

,

z

=

75°
(iv)

x

=

62°

,

y

=

45°

,

z

=

73°
(v)

x

=

58°

,

y

=

45°

,

z

=

77°

Question 13

13.

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

(i)

x

=

59°

,

y

=

74°
(ii)

x

=

60°

,

y

=

75°
(iii)

x

=

61°

,

y

=

76°
(iv)

x

=

58°

,

y

=

73°
(v)

x

=

62°

,

y

=

77°

Question 14

14.

Calculate the value of the lettered angle in the following figure

(i)

x

=

62.17°
(ii)

x

=

59.17°
(iii)

x

=

60.17°
(iv)

x

=

58.17°
(v)

x

=

61.17°

Question 15

15.

Calculate the value of the lettered angle in the following figure

(i)

x

=

49.29°
(ii)

x

=

50.29°
(iii)

x

=

52.29°
(iv)

x

=

51.29°
(v)

x

=

48.29°

Question 16

16.

In the given triangle, ∠B = 45.84°. Find the measure of ∠C and ∠D

(i)

∠C = ∠D = 68.08°
(ii)

∠C = ∠D = 66.08°
(iii)

∠C = ∠D = 65.08°
(iv)

∠C = ∠D = 69.08°
(v)

∠C = ∠D = 67.08°

Question 17

17.

Find the unknown angle in the following figure

(i)

x

=

50.28°
(ii)

x

=

51.28°
(iii)

x

=

49.28°
(iv)

x

=

52.28°
(v)

x

=

53.28°

Question 18

18.

Find the unknown angle in the following figure

(i)

x

=

91°
(ii)

x

=

88°
(iii)

x

=

90°
(iv)

x

=

92°
(v)

x

=

89°

Question 19

19.

Find the unknown angle in the following figure

(i)

x

=

134°
(ii)

x

=

133°
(iii)

x

=

136°
(iv)

x

=

135°
(v)

x

=

137°

Question 20

20.

In △FGH, if ∠F = 54° and ∠G = 52°, find the measure of ∠H

(i)

H

=

73°
(ii)

H

=

75°
(iii)

H

=

76°
(iv)

H

=

74°
(v)

H

=

72°

Question 21

21.

In △CDE, if ∠C = 80° and ∠D = ∠E, find the measure of each of the equal angles of the triangle

(i)

49°
(ii)

50°
(iii)

51°
(iv)

52°
(v)

48°

Question 22

22.

One angle of a triangle measures 36° and the other two angles are in the ratio 5 : 11. Find these angles.

(i)

B

=

43°

,

C

=

97°
(ii)

B

=

46°

,

C

=

100°
(iii)

B

=

47°

,

C

=

101°
(iv)

B

=

44°

,

C

=

98°
(v)

B

=

45°

,

C

=

99°

Question 23

23.

In a right-angled triangle, the two acute angles are in the ratio 5 : 13. Find these angles.

(i)

A

=

26°

,

C

=

66°
(ii)

A

=

25°

,

C

=

65°
(iii)

A

=

27°

,

C

=

67°
(iv)

A

=

23°

,

C

=

63°
(v)

A

=

24°

,

C

=

64°

Question 24

24.

One of the two equal angles of an isosceles triangle measures 66°. Find the measure of each angle of the triangle.

(i)

A

=

66°

,

B

=

66°

,

C

=

48°
(ii)

A

=

68°

,

B

=

66°

,

C

=

46°
(iii)

A

=

64°

,

B

=

68°

,

C

=

48°
(iv)

A

=

64°

,

B

=

66°

,

C

=

50°
(v)

A

=

66°

,

B

=

64°

,

C

=

50°

Question 25

25.

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

(i)

43°
(ii)

46°
(iii)

44°
(iv)

47°
(v)

45°

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)

61°
(ii)

59°
(iii)

58°
(iv)

62°
(v)

60°

Question 27

27.

In a right-angled triangle if one of the acute angles is 45°, find the measure of the other acute angle.

(i)

47°
(ii)

45°
(iii)

44°
(iv)

43°
(v)

46°

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

=

118°

,

B

=

32°

,

C

=

30°
(iv)

A

=

120°

,

B

=

30°

,

C

=

30°
(v)

A

=

118°

,

B

=

30°

,

C

=

32°

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 1 : 1. Find each angle of the triangle

(i)

A

=

60°

,

B

=

60°

,

C

=

60°
(ii)

A

=

62°

,

B

=

60°

,

C

=

58°
(iii)

A

=

60°

,

B

=

58°

,

C

=

62°
(iv)

A

=

58°

,

B

=

60°

,

C

=

62°
(v)

A

=

58°

,

B

=

62°

,

C

=

60°

Question 31

31.

In the given figure, find ∠KLJ

(i)

54°
(ii)

57°
(iii)

55°
(iv)

53°
(v)

56°

Question 32

32.

In the given figure, find ∠LJK

(i)

103°
(ii)

104°
(iii)

105°
(iv)

102°
(v)

101°

Question 33

33.

In the given figure, find ∠KLJ

(i)

35°
(ii)

36°
(iii)

37°
(iv)

38°
(v)

39°

Question 34

34.

In the given figure, find ∠GKJ

(i)

137°
(ii)

139°
(iii)

140°
(iv)

141°
(v)

138°

Question 35

35.

In the given figure , if LI ⟂ JK and ∠IJL = 57.99°, find ∠LIJ

(i)

34.01°
(ii)

30.01°
(iii)

33.01°
(iv)

31.01°
(v)

32.01°

Question 36

36.

In the given figure , if IF ⟂ GH and ∠FGI = 39.58°, find ∠HFI

(i)

35.97°
(ii)

37.97°
(iii)

36.97°
(iv)

33.97°
(v)

34.97°

Question 37

37.

In the given figure , if HE ⟂ FG and ∠EFH = 45°, find ∠HGE

(i)

58.04°
(ii)

57.04°
(iii)

61.04°
(iv)

60.04°
(v)

59.04°

Question 38

38.

In below given figure, find ∠ILK

(i)

119.86°
(ii)

116.86°
(iii)

117.86°
(iv)

120.86°
(v)

118.86°

Question 39

39.

In below given figure, find ∠MJK

(i)

72.04°
(ii)

74.04°
(iii)

73.04°
(iv)

75.04°
(v)

71.04°

Question 40

40.

In below given figure, find ∠JHL

(i)

91.84°
(ii)

93.84°
(iii)

92.84°
(iv)

90.84°
(v)

94.84°

Question 41

41.

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

(i)

x

=

46.13°

,

y

=

69.94°
(ii)

x

=

45.13°

,

y

=

68.94°
(iii)

x

=

43.13°

,

y

=

66.94°
(iv)

x

=

47.13°

,

y

=

70.94°
(v)

x

=

44.13°

,

y

=

67.94°

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

=

45°

,

Y

=

88°

,

Z

=

47°
(ii)

X

=

47°

,

Y

=

90°

,

Z

=

43°
(iii)

X

=

45°

,

Y

=

90°

,

Z

=

45°
(iv)

X

=

43°

,

Y

=

90°

,

Z

=

47°
(v)

X

=

43°

,

Y

=

92°

,

Z

=

45°

Question 43

43.

(i)

122°
(ii)

119°
(iii)

118°
(iv)

120°
(v)

121°

Question 44

44.

In the given figure, △ABC is a triangle in which ∠B = 68.07° and ∠C = 70.19°.

If 'z' is the angle between the bisector of ∠B and ∠C, then find z.

(i)

110.87°
(ii)

111.87°
(iii)

109.87°
(iv)

112.87°
(v)

108.87°

Question 45

45.

In the given figure, ∠L = 44.78° and ∠M = 70.08°.

Side MN is produced to O, so that ∠MNL and ∠LNO form a linear pair.

(i)

x

=

34.57°

,

y

=

59.43°
(ii)

x

=

33.57°

,

y

=

58.43°
(iii)

x

=

31.57°

,

y

=

56.43°
(iv)

x

=

32.57°

,

y

=

57.43°
(v)

x

=

30.57°

,

y

=

55.43°

Question 46

46.

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

(i)

x

=

41.22°

,

y

=

48.63°
(ii)

x

=

42.22°

,

y

=

49.63°
(iii)

x

=

44.22°

,

y

=

51.63°
(iv)

x

=

40.22°

,

y

=

47.63°
(v)

x

=

43.22°

,

y

=

50.63°

Question 47

47.

In the given figure, △DEF in which ∠E = 57.84° and ∠F = 63.09°. DG and EF bisects each other. Find the value of z

(i)

z

=

61.07°
(ii)

z

=

57.07°
(iii)

z

=

58.07°
(iv)

z

=

60.07°
(v)

z

=

59.07°

Question 48

48.

In the given figure, MN ∥ OP, ∠JGN = 59° and GH = IG. Find the measure of x.

(i)

x

=

60°
(ii)

x

=

61°
(iii)

x

=

64°
(iv)

x

=

62°
(v)

x

=

63°

Question 49

49.

In the given figure, find the value of x.

(i)

x

=

25°
(ii)

x

=

23°
(iii)

x

=

24°
(iv)

x

=

21°
(v)

x

=

22°

Question 50

50.

In the given figure, BC ∥ DE and BD = DF. Find the values of x,y and z.

(i)

x

=

29°

,

y

=

70°

,

z

=

42°
(ii)

x

=

31°

,

y

=

68°

,

z

=

42°
(iii)

x

=

33°

,

y

=

70°

,

z

=

38°
(iv)

x

=

31°

,

y

=

70°

,

z

=

40°
(v)

x

=

29°

,

y

=

72°

,

z

=

40°

Question 51

51.

In the given figure, if MK = KN = LN. Find the value of x.

(i)

x

=

72.5°
(ii)

x

=

74.5°
(iii)

x

=

71.5°
(iv)

x

=

73.5°
(v)

x

=

75.5°

Question 52

52.

In the given figure, if HF = HI = IG, find the value of x

(i)

x

=

39°
(ii)

x

=

38°
(iii)

x

=

42°
(iv)

x

=

40°
(v)

x

=

41°

Question 53

53.

In the given figure, if IF = GI and FJ = JH , find the value of x.

(i)

x

=

61.94°
(ii)

x

=

58.94°
(iii)

x

=

59.94°
(iv)

x

=

62.94°
(v)

x

=

60.94°

Question 54

54.

In the given figure, if AD = EA, find the values of x , y , z and t

(i)

x =67.62°, y =26.19°, z =24.8° , t =122.81°
(ii)

x =67.62°, y =26.19°, z =25.8° , t =123.81°
(iii)

x =67.62°, y =26.19°, z =26.8° , t =124.81°
(iv)

x =67.62°, y =24.19°, z =23.8° , t =123.81°
(v)

x =67.62°, y =28.19°, z =27.8° , t =123.81°

Question 55

55.

In the given figure, calculate the value of x.

(i)

x

=

18°
(ii)

x

=

22°
(iii)

x

=

21°
(iv)

x

=

19°
(v)

x

=

20°

Question 56

56.

In the given figure, calculate the value of x.

(i)

x

=

71.89°
(ii)

x

=

69.89°
(iii)

x

=

70.89°
(iv)

x

=

68.89°
(v)

x

=

72.89°

Question 57

57.

In the given figure, calculate the value of x.

(i)

x

=

64.67°
(ii)

x

=

65.67°
(iii)

x

=

68.67°
(iv)

x

=

66.67°
(v)

x

=

67.67°

Question 58

58.

Find the unknown marked angles in the following figure

(i)

x

=

110°

,

y

=

39°
(ii)

x

=

107°

,

y

=

36°
(iii)

x

=

111°

,

y

=

40°
(iv)

x

=

108°

,

y

=

37°
(v)

x

=

109°

,

y

=

38°

Question 59

59.

Find the unknown marked angles in the following figure

(i)

x

=

117°

,

y

=

117°
(ii)

x

=

116°

,

y

=

116°
(iii)

x

=

114°

,

y

=

114°
(iv)

x

=

115°

,

y

=

115°
(v)

x

=

113°

,

y

=

113°

Question 60

60.

In the given figure, calculate the value of x.

(i)

x

=

138°
(ii)

x

=

139°
(iii)

x

=

142°
(iv)

x

=

141°
(v)

x

=

140°

Question 61

61.

In the given figure, calculate the value of x.

(i)

x

=

23.5°
(ii)

x

=

24.5°
(iii)

x

=

20.5°
(iv)

x

=

22.5°
(v)

x

=

21.5°

Question 62

62.

Find the unknown marked angles in the following figure

(i)

x

=

119°

,

y

=

152°
(ii)

x

=

118°

,

y

=

151°
(iii)

x

=

116°

,

y

=

149°
(iv)

x

=

115°

,

y

=

148°
(v)

x

=

117°

,

y

=

150°

Question 63

63.

In the following figure HI ∥ KJ, find the values of x and y.

(i)

x

=

35°

,

y

=

113°
(ii)

x

=

36°

,

y

=

114°
(iii)

x

=

33°

,

y

=

111°
(iv)

x

=

32°

,

y

=

110°
(v)

x

=

34°

,

y

=

112°

Question 64

64.

Find the unknown marked angles in the following figure

(i)

x

=

87°

,

y

=

110°
(ii)

x

=

89°

,

y

=

112°
(iii)

x

=

88°

,

y

=

111°
(iv)

x

=

91°

,

y

=

114°
(v)

x

=

90°

,

y

=

113°

Question 65

65.

In the given figure, it is given that CB ∥ ED , ∠CED = 76° and ∠CBA = 76°. Find the value of x.

(i)

x

=

30°
(ii)

x

=

26°
(iii)

x

=

28°
(iv)

x

=

27°
(v)

x

=

29°

Question 66

66.

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

(i)

x

=

37°

,

y

=

39°

,

z

=

72°
(ii)

x

=

35°

,

y

=

37°

,

z

=

76°
(iii)

x

=

35°

,

y

=

39°

,

z

=

74°
(iv)

x

=

33°

,

y

=

41°

,

z

=

74°
(v)

x

=

33°

,

y

=

39°

,

z

=

76°

Question 67

67.

Find the value of x in the given figure.

(i)

x

=

29°
(ii)

x

=

28°
(iii)

x

=

26°
(iv)

x

=

27°
(v)

x

=

25°

Question 68

68.

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

(i)

x

=

78°

,

y

=

59°

,

z

=

64°
(ii)

x

=

82°

,

y

=

59°

,

z

=

60°
(iii)

x

=

80°

,

y

=

57°

,

z

=

64°
(iv)

x

=

80°

,

y

=

59°

,

z

=

62°
(v)

x

=

78°

,

y

=

61°

,

z

=

62°

Question 69

69.

In the given two equilateral triangles, find ∠M + ∠O + ∠Q + ∠N + ∠P + ∠R .

(i)

360°
(ii)

359°
(iii)

361°
(iv)

362°
(v)

358°

Question 70

70.

In a right angled triangle, if one of the angles is 56.31°, find the third angle

(i)

33.69°
(ii)

48.69°
(iii)

38.69°
(iv)

43.69°
(v)

63.69°

Question 71

71.

In a right angled triangle, if one of the angles is 42.51°, find the third angle

(i)

52.49°
(ii)

62.49°
(iii)

47.49°
(iv)

57.49°
(v)

77.49°

Assignment Key