EduSahara™ Worksheet

Question 1

1.

Two angles of a triangle measure 59° and 55° respectively. Find the measure of the third angle of the triangle

(i)

65°
(ii)

64°
(iii)

66°
(iv)

68°
(v)

67°

Question 2

2.

The angles of a triangle ABC are in the ratio 3 : 25 : 32. Find the measure of each angle of the triangle

(i)

A

=

9°

,

B

=

75°

,

C

=

96°
(ii)

A

=

9°

,

B

=

73°

,

C

=

98°
(iii)

A

=

7°

,

B

=

77°

,

C

=

96°
(iv)

A

=

7°

,

B

=

75°

,

C

=

98°
(v)

A

=

11°

,

B

=

75°

,

C

=

94°

Question 3

3.

Find the unknown angle from the following figure

(i)

x

=

64.87°
(ii)

x

=

61.87°
(iii)

x

=

65.87°
(iv)

x

=

62.87°
(v)

x

=

63.87°

Question 4

4.

In the given figure, △FGH in which side GH has been produced to I. If ∠HFG = x° , ∠FGH = (7/3a)° , ∠GHF = (5/3a)° and ∠FHI = (13/3a)°, find the values of a and x.

(i)

a

=

32°

,

x

=

62°
(ii)

a

=

29°

,

x

=

59°
(iii)

a

=

30°

,

x

=

60°
(iv)

a

=

31°

,

x

=

61°
(v)

a

=

28°

,

x

=

58°

Question 5

5.

Find the angles of the triangle

(i)

H

=

58°

,

I

=

47°

,

J

=

75°
(ii)

H

=

60°

,

I

=

43°

,

J

=

77°
(iii)

H

=

62°

,

I

=

45°

,

J

=

73°
(iv)

H

=

60°

,

I

=

45°

,

J

=

75°
(v)

H

=

58°

,

I

=

45°

,

J

=

77°

Question 6

6.

Calculate the value of x in the following figure

(i)

x

=

50.8°
(ii)

x

=

53.8°
(iii)

x

=

49.8°
(iv)

x

=

52.8°
(v)

x

=

51.8°

Question 7

7.

Calculate the value of x in the following figure

(i)

x

=

84.03°
(ii)

x

=

81.03°
(iii)

x

=

83.03°
(iv)

x

=

82.03°
(v)

x

=

85.03°

Question 8

8.

Find the unknown marked angle in the following figure

(i)

x

=

55.95°
(ii)

x

=

53.95°
(iii)

x

=

54.95°
(iv)

x

=

56.95°
(v)

x

=

52.95°

Question 9

9.

Find the unknown angles in the following figure

(i)

A

=

49°

,

B

=

49°
(ii)

A

=

50°

,

B

=

50°
(iii)

A

=

48°

,

B

=

48°
(iv)

A

=

52°

,

B

=

52°
(v)

A

=

51°

,

B

=

51°

Question 10

10.

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

(i)

I

=

60°

,

J

=

45°

,

K

=

75°
(ii)

I

=

62°

,

J

=

45°

,

K

=

73°
(iii)

I

=

58°

,

J

=

45°

,

K

=

77°
(iv)

I

=

58°

,

J

=

47°

,

K

=

75°
(v)

I

=

60°

,

J

=

43°

,

K

=

77°

Question 11

11.

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

(i)

L

=

60°

,

M

=

45°

,

N

=

75°
(ii)

L

=

58°

,

M

=

47°

,

N

=

75°
(iii)

L

=

58°

,

M

=

45°

,

N

=

77°
(iv)

L

=

62°

,

M

=

45°

,

N

=

73°
(v)

L

=

60°

,

M

=

43°

,

N

=

77°

Question 12

12.

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

(i)

x

=

38°

,

y

=

45°

,

z

=

97°
(ii)

x

=

42°

,

y

=

45°

,

z

=

93°
(iii)

x

=

40°

,

y

=

43°

,

z

=

97°
(iv)

x

=

40°

,

y

=

45°

,

z

=

95°
(v)

x

=

38°

,

y

=

47°

,

z

=

95°

Question 13

13.

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

(i)

x

=

44°

,

y

=

98°
(ii)

x

=

46°

,

y

=

100°
(iii)

x

=

45°

,

y

=

99°
(iv)

x

=

47°

,

y

=

101°
(v)

x

=

43°

,

y

=

97°

Question 14

14.

Calculate the value of the lettered angle in the following figure

(i)

x

=

46.73°
(ii)

x

=

43.73°
(iii)

x

=

45.73°
(iv)

x

=

42.73°
(v)

x

=

44.73°

Question 15

15.

Calculate the value of the lettered angle in the following figure

(i)

x

=

45°
(ii)

x

=

47°
(iii)

x

=

43°
(iv)

x

=

44°
(v)

x

=

46°

Question 16

16.

In the given triangle, ∠C = 42.24°. Find the measure of ∠D and ∠E

(i)

∠D = ∠E = 68.88°
(ii)

∠D = ∠E = 70.88°
(iii)

∠D = ∠E = 69.88°
(iv)

∠D = ∠E = 67.88°
(v)

∠D = ∠E = 66.88°

Question 17

17.

Find the unknown angle in the following figure

(i)

x

=

88.1°
(ii)

x

=

85.1°
(iii)

x

=

84.1°
(iv)

x

=

87.1°
(v)

x

=

86.1°

Question 18

18.

Find the unknown angle in the following figure

(i)

x

=

91°
(ii)

x

=

90°
(iii)

x

=

92°
(iv)

x

=

88°
(v)

x

=

89°

Question 19

19.

Find the unknown angle in the following figure

(i)

x

=

135°
(ii)

x

=

136°
(iii)

x

=

133°
(iv)

x

=

137°
(v)

x

=

134°

Question 20

20.

In △ABC, if ∠A = 50° and ∠B = 70°, find the measure of ∠C

(i)

C

=

59°
(ii)

C

=

61°
(iii)

C

=

62°
(iv)

C

=

60°
(v)

C

=

58°

Question 21

21.

In △ABC, if ∠A = 30° and ∠B = ∠C, find the measure of each of the equal angles of the triangle

(i)

77°
(ii)

75°
(iii)

73°
(iv)

76°
(v)

74°

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

=

47°

,

C

=

101°
(ii)

B

=

43°

,

C

=

97°
(iii)

B

=

45°

,

C

=

99°
(iv)

B

=

46°

,

C

=

100°
(v)

B

=

44°

,

C

=

98°

Question 23

23.

In a right-angled triangle, the two acute angles are in the ratio 2 : 7. Find these angles.

(i)

A

=

19°

,

C

=

69°
(ii)

A

=

22°

,

C

=

72°
(iii)

A

=

21°

,

C

=

71°
(iv)

A

=

20°

,

C

=

70°
(v)

A

=

18°

,

C

=

68°

Question 24

24.

One of the two equal angles of an isosceles triangle measures 71°. Find the measure of each angle of the triangle.

(i)

A

=

73°

,

B

=

71°

,

C

=

36°
(ii)

A

=

71°

,

B

=

71°

,

C

=

38°
(iii)

A

=

71°

,

B

=

69°

,

C

=

40°
(iv)

A

=

69°

,

B

=

73°

,

C

=

38°
(v)

A

=

69°

,

B

=

71°

,

C

=

40°

Question 25

25.

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

(i)

45°
(ii)

46°
(iii)

43°
(iv)

47°
(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)

60°
(ii)

62°
(iii)

58°
(iv)

59°
(v)

61°

Question 27

27.

In a right-angled triangle if one of the acute angles is 59°, find the measure of the other acute angle.

(i)

31°
(ii)

29°
(iii)

32°
(iv)

33°
(v)

30°

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

=

30°

,

C

=

30°
(ii)

A

=

118°

,

B

=

32°

,

C

=

30°
(iii)

A

=

120°

,

B

=

28°

,

C

=

32°
(iv)

A

=

118°

,

B

=

30°

,

C

=

32°
(v)

A

=

122°

,

B

=

30°

,

C

=

28°

Question 29

29.

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

(i)

A

=

18°

,

B

=

80°

,

C

=

82°
(ii)

A

=

22°

,

B

=

80°

,

C

=

78°
(iii)

A

=

20°

,

B

=

78°

,

C

=

82°
(iv)

A

=

18°

,

B

=

82°

,

C

=

80°
(v)

A

=

20°

,

B

=

80°

,

C

=

80°

Question 30

30.

The ratio between the base angle and the vertical angle of an isosceles triangle is 1 : 2. Find each angle of the triangle

(i)

A

=

88°

,

B

=

45°

,

C

=

47°
(ii)

A

=

88°

,

B

=

47°

,

C

=

45°
(iii)

A

=

92°

,

B

=

45°

,

C

=

43°
(iv)

A

=

90°

,

B

=

43°

,

C

=

47°
(v)

A

=

90°

,

B

=

45°

,

C

=

45°

Question 31

31.

In the given figure, find ∠EFD

(i)

76°
(ii)

80°
(iii)

78°
(iv)

77°
(v)

79°

Question 32

32.

In the given figure, find ∠FDE

(i)

109°
(ii)

110°
(iii)

107°
(iv)

108°
(v)

111°

Question 33

33.

In the given figure, find ∠HIG

(i)

59°
(ii)

60°
(iii)

62°
(iv)

61°
(v)

58°

Question 34

34.

In the given figure, find ∠KON

(i)

148°
(ii)

149°
(iii)

150°
(iv)

146°
(v)

147°

Question 35

35.

In the given figure , if EB ⟂ CD and ∠BCE = 45°, find ∠EBC

(i)

46.00°
(ii)

45.00°
(iii)

47.00°
(iv)

44.00°
(v)

43.00°

Question 36

36.

In the given figure , if GD ⟂ EF and ∠DEG = 53.13°, find ∠FDG

(i)

22.23°
(ii)

24.23°
(iii)

25.23°
(iv)

26.23°
(v)

23.23°

Question 37

37.

In the given figure , if LI ⟂ JK and ∠IJL = 46.31°, find ∠LKI

(i)

60.18°
(ii)

59.18°
(iii)

58.18°
(iv)

61.18°
(v)

62.18°

Question 38

38.

In below given figure, find ∠FIH

(i)

117.95°
(ii)

114.95°
(iii)

115.95°
(iv)

116.95°
(v)

118.95°

Question 39

39.

In below given figure, find ∠MJK

(i)

44.79°
(ii)

40.79°
(iii)

41.79°
(iv)

43.79°
(v)

42.79°

Question 40

40.

In below given figure, find ∠JHL

(i)

83.97°
(ii)

86.97°
(iii)

85.97°
(iv)

84.97°
(v)

87.97°

Question 41

41.

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

(i)

x

=

111.91°

,

y

=

72.09°
(ii)

x

=

107.91°

,

y

=

68.09°
(iii)

x

=

108.91°

,

y

=

69.09°
(iv)

x

=

109.91°

,

y

=

70.09°
(v)

x

=

110.91°

,

y

=

71.09°

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

=

43°

,

Y

=

92°

,

Z

=

45°
(iii)

X

=

45°

,

Y

=

90°

,

Z

=

45°
(iv)

X

=

47°

,

Y

=

90°

,

Z

=

43°
(v)

X

=

43°

,

Y

=

90°

,

Z

=

47°

Question 43

43.

(i)

118°
(ii)

119°
(iii)

120°
(iv)

121°
(v)

122°

Question 44

44.

In the given figure, △CDE is a triangle in which ∠D = 68.68° and ∠E = 60.22°.

If 'z' is the angle between the bisector of ∠D and ∠E, then find z.

(i)

113.55°
(ii)

117.55°
(iii)

116.55°
(iv)

114.55°
(v)

115.55°

Question 45

45.

In the given figure, ∠A = 52.66° and ∠B = 60.12°.

Side BC is produced to D, so that ∠BCA and ∠ACD form a linear pair.

(i)

x

=

35.61°

,

y

=

58.39°
(ii)

x

=

31.61°

,

y

=

54.39°
(iii)

x

=

32.61°

,

y

=

55.39°
(iv)

x

=

34.61°

,

y

=

57.39°
(v)

x

=

33.61°

,

y

=

56.39°

Question 46

46.

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

(i)

x

=

42.01°

,

y

=

44.77°
(ii)

x

=

40.01°

,

y

=

42.77°
(iii)

x

=

44.01°

,

y

=

46.77°
(iv)

x

=

41.01°

,

y

=

43.77°
(v)

x

=

43.01°

,

y

=

45.77°

Question 47

47.

In the given figure, △CDE in which ∠D = 50.13° and ∠E = 50.88°. CF and DE bisects each other. Find the value of z

(i)

z

=

79.99°
(ii)

z

=

77.99°
(iii)

z

=

80.99°
(iv)

z

=

76.99°
(v)

z

=

78.99°

Question 48

48.

In the given figure, MN ∥ OP, ∠GDN = 62° and DE = FD. Find the measure of x.

(i)

x

=

55°
(ii)

x

=

57°
(iii)

x

=

56°
(iv)

x

=

54°
(v)

x

=

58°

Question 49

49.

In the given figure, find the value of x.

(i)

x

=

133°
(ii)

x

=

131°
(iii)

x

=

130°
(iv)

x

=

134°
(v)

x

=

132°

Question 50

50.

In the given figure, KL ∥ MN and KM = MO. Find the values of x,y and z.

(i)

x

=

29°

,

y

=

65°

,

z

=

52°
(ii)

x

=

33°

,

y

=

65°

,

z

=

48°
(iii)

x

=

31°

,

y

=

65°

,

z

=

50°
(iv)

x

=

31°

,

y

=

63°

,

z

=

52°
(v)

x

=

29°

,

y

=

67°

,

z

=

50°

Question 51

51.

In the given figure, if HF = FI = GI. Find the value of x.

(i)

x

=

67°
(ii)

x

=

71°
(iii)

x

=

70°
(iv)

x

=

68°
(v)

x

=

69°

Question 52

52.

In the given figure, if KI = KL = LJ, find the value of x

(i)

x

=

22°
(ii)

x

=

20°
(iii)

x

=

18°
(iv)

x

=

21°
(v)

x

=

19°

Question 53

53.

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

(i)

x

=

56.62°
(ii)

x

=

54.62°
(iii)

x

=

58.62°
(iv)

x

=

57.62°
(v)

x

=

55.62°

Question 54

54.

In the given figure, if MP = QM, find the values of x , y , z and t

(i)

x =43.5°, y =25.7°, z =24.94° , t =111.75°
(ii)

x =43.5°, y =23.7°, z =22.94° , t =111.75°
(iii)

x =43.5°, y =21.7°, z =20.94° , t =111.75°
(iv)

x =43.5°, y =23.7°, z =21.94° , t =110.75°
(v)

x =43.5°, y =23.7°, z =23.94° , t =112.75°

Question 55

55.

In the given figure, calculate the value of x.

(i)

x

=

24°
(ii)

x

=

23°
(iii)

x

=

25°
(iv)

x

=

26°
(v)

x

=

27°

Question 56

56.

In the given figure, calculate the value of x.

(i)

x

=

73.57°
(ii)

x

=

72.57°
(iii)

x

=

71.57°
(iv)

x

=

74.57°
(v)

x

=

70.57°

Question 57

57.

In the given figure, calculate the value of x.

(i)

x

=

42.57°
(ii)

x

=

40.57°
(iii)

x

=

39.57°
(iv)

x

=

41.57°
(v)

x

=

43.57°

Question 58

58.

Find the unknown marked angles in the following figure

(i)

x

=

103°

,

y

=

28°
(ii)

x

=

107°

,

y

=

32°
(iii)

x

=

106°

,

y

=

31°
(iv)

x

=

104°

,

y

=

29°
(v)

x

=

105°

,

y

=

30°

Question 59

59.

Find the unknown marked angles in the following figure

(i)

x

=

111°

,

y

=

111°
(ii)

x

=

108°

,

y

=

108°
(iii)

x

=

107°

,

y

=

107°
(iv)

x

=

109°

,

y

=

109°
(v)

x

=

110°

,

y

=

110°

Question 60

60.

In the given figure, calculate the value of x.

(i)

x

=

149°
(ii)

x

=

147°
(iii)

x

=

150°
(iv)

x

=

148°
(v)

x

=

146°

Question 61

61.

In the given figure, calculate the value of x.

(i)

x

=

21.5°
(ii)

x

=

22.5°
(iii)

x

=

23.5°
(iv)

x

=

20.5°
(v)

x

=

24.5°

Question 62

62.

Find the unknown marked angles in the following figure

(i)

x

=

101°

,

y

=

151°
(ii)

x

=

98°

,

y

=

148°
(iii)

x

=

100°

,

y

=

150°
(iv)

x

=

102°

,

y

=

152°
(v)

x

=

99°

,

y

=

149°

Question 63

63.

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

(i)

x

=

48°

,

y

=

90°
(ii)

x

=

47°

,

y

=

89°
(iii)

x

=

46°

,

y

=

88°
(iv)

x

=

44°

,

y

=

86°
(v)

x

=

45°

,

y

=

87°

Question 64

64.

Find the unknown marked angles in the following figure

(i)

x

=

85°

,

y

=

111°
(ii)

x

=

87°

,

y

=

113°
(iii)

x

=

89°

,

y

=

115°
(iv)

x

=

88°

,

y

=

114°
(v)

x

=

86°

,

y

=

112°

Question 65

65.

In the given figure, it is given that JI ∥ LK , ∠JLK = 71° and ∠JIH = 83°. Find the value of x.

(i)

x

=

26°
(ii)

x

=

24°
(iii)

x

=

27°
(iv)

x

=

25°
(v)

x

=

28°

Question 66

66.

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

(i)

x

=

26°

,

y

=

40°

,

z

=

62°
(ii)

x

=

22°

,

y

=

42°

,

z

=

64°
(iii)

x

=

24°

,

y

=

38°

,

z

=

66°
(iv)

x

=

22°

,

y

=

40°

,

z

=

66°
(v)

x

=

24°

,

y

=

40°

,

z

=

64°

Question 67

67.

Find the value of x in the given figure.

(i)

x

=

19°
(ii)

x

=

23°
(iii)

x

=

21°
(iv)

x

=

20°
(v)

x

=

22°

Question 68

68.

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

(i)

x

=

82°

,

y

=

59°

,

z

=

60°
(ii)

x

=

80°

,

y

=

63°

,

z

=

58°
(iii)

x

=

80°

,

y

=

61°

,

z

=

60°
(iv)

x

=

82°

,

y

=

61°

,

z

=

58°
(v)

x

=

84°

,

y

=

61°

,

z

=

56°

Question 69

69.

In the given two equilateral triangles, find ∠G + ∠I + ∠K + ∠H + ∠J + ∠L .

(i)

361°
(ii)

359°
(iii)

360°
(iv)

358°
(v)

362°

Question 70

70.

In a right angled triangle, if one of the angles is 49.76°, find the third angle

(i)

70.24°
(ii)

40.24°
(iii)

45.24°
(iv)

55.24°
(v)

50.24°

Question 71

71.

In a right angled triangle, if one of the angles is 40.91°, find the third angle

(i)

59.09°
(ii)

54.09°
(iii)

49.09°
(iv)

64.09°
(v)

79.09°

Assignment Key