EduSahara™ Worksheet

Question 1

1.

Two angles of a triangle measure 69° and 55° respectively. Find the measure of the third angle of the triangle

(i)

55°
(ii)

54°
(iii)

57°
(iv)

56°
(v)

58°

Question 2

2.

The angles of a triangle ABC are in the ratio 5 : 8 : 47. Find the measure of each angle of the triangle

(i)

A

=

15°

,

B

=

22°

,

C

=

143°
(ii)

A

=

13°

,

B

=

26°

,

C

=

141°
(iii)

A

=

17°

,

B

=

24°

,

C

=

139°
(iv)

A

=

15°

,

B

=

24°

,

C

=

141°
(v)

A

=

13°

,

B

=

24°

,

C

=

143°

Question 3

3.

Find the unknown angle from the following figure

(i)

x

=

57.7°
(ii)

x

=

54.7°
(iii)

x

=

56.7°
(iv)

x

=

55.7°
(v)

x

=

53.7°

Question 4

4.

In the given figure, △IJK in which side JK has been produced to L. If ∠KIJ = x° , ∠IJK = (2a)° , ∠JKI = (7/2a)° and ∠IKL = (11/2a)°, find the values of a and x.

(i)

a

=

21°

,

x

=

71°
(ii)

a

=

18°

,

x

=

68°
(iii)

a

=

19°

,

x

=

69°
(iv)

a

=

22°

,

x

=

72°
(v)

a

=

20°

,

x

=

70°

Question 5

5.

Find the angles of the triangle

(i)

H

=

57°

,

I

=

35°

,

J

=

88°
(ii)

H

=

55°

,

I

=

33°

,

J

=

92°
(iii)

H

=

53°

,

I

=

37°

,

J

=

90°
(iv)

H

=

53°

,

I

=

35°

,

J

=

92°
(v)

H

=

55°

,

I

=

35°

,

J

=

90°

Question 6

6.

Calculate the value of x in the following figure

(i)

x

=

74°
(ii)

x

=

72°
(iii)

x

=

73°
(iv)

x

=

71°
(v)

x

=

70°

Question 7

7.

Calculate the value of x in the following figure

(i)

x

=

86.13°
(ii)

x

=

87.13°
(iii)

x

=

84.13°
(iv)

x

=

85.13°
(v)

x

=

83.13°

Question 8

8.

Find the unknown marked angle in the following figure

(i)

x

=

46.44°
(ii)

x

=

45.44°
(iii)

x

=

48.44°
(iv)

x

=

47.44°
(v)

x

=

44.44°

Question 9

9.

Find the unknown angles in the following figure

(i)

B

=

47°

,

C

=

47°
(ii)

B

=

46°

,

C

=

46°
(iii)

B

=

50°

,

C

=

50°
(iv)

B

=

49°

,

C

=

49°
(v)

B

=

48°

,

C

=

48°

Question 10

10.

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

(i)

C

=

60°

,

D

=

43°

,

E

=

77°
(ii)

C

=

62°

,

D

=

45°

,

E

=

73°
(iii)

C

=

58°

,

D

=

45°

,

E

=

77°
(iv)

C

=

58°

,

D

=

47°

,

E

=

75°
(v)

C

=

60°

,

D

=

45°

,

E

=

75°

Question 11

11.

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

(i)

C

=

30°

,

D

=

53°

,

E

=

97°
(ii)

C

=

28°

,

D

=

57°

,

E

=

95°
(iii)

C

=

28°

,

D

=

55°

,

E

=

97°
(iv)

C

=

32°

,

D

=

55°

,

E

=

93°
(v)

C

=

30°

,

D

=

55°

,

E

=

95°

Question 12

12.

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

(i)

x

=

25°

,

y

=

53°

,

z

=

102°
(ii)

x

=

25°

,

y

=

55°

,

z

=

100°
(iii)

x

=

23°

,

y

=

57°

,

z

=

100°
(iv)

x

=

27°

,

y

=

55°

,

z

=

98°
(v)

x

=

23°

,

y

=

55°

,

z

=

102°

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

=

74°
(ii)

x

=

46°

,

y

=

76°
(iii)

x

=

47°

,

y

=

77°
(iv)

x

=

45°

,

y

=

75°
(v)

x

=

43°

,

y

=

73°

Question 14

14.

Calculate the value of the lettered angle in the following figure

(i)

x

=

44.3°
(ii)

x

=

46.3°
(iii)

x

=

45.3°
(iv)

x

=

43.3°
(v)

x

=

47.3°

Question 15

15.

Calculate the value of the lettered angle in the following figure

(i)

x

=

33.89°
(ii)

x

=

36.89°
(iii)

x

=

37.89°
(iv)

x

=

34.89°
(v)

x

=

35.89°

Question 16

16.

In the given triangle, ∠I = 92.06°. Find the measure of ∠J and ∠K

(i)

∠J = ∠K = 43.97°
(ii)

∠J = ∠K = 44.97°
(iii)

∠J = ∠K = 45.97°
(iv)

∠J = ∠K = 41.97°
(v)

∠J = ∠K = 42.97°

Question 17

17.

Find the unknown angle in the following figure

(i)

x

=

40.04°
(ii)

x

=

43.04°
(iii)

x

=

42.04°
(iv)

x

=

39.04°
(v)

x

=

41.04°

Question 18

18.

Find the unknown angle in the following figure

(i)

x

=

44°
(ii)

x

=

45°
(iii)

x

=

46°
(iv)

x

=

43°
(v)

x

=

47°

Question 19

19.

Find the unknown angle in the following figure

(i)

x

=

136°
(ii)

x

=

133°
(iii)

x

=

135°
(iv)

x

=

134°
(v)

x

=

137°

Question 20

20.

In △ABC, if ∠A = 62° and ∠B = 57°, find the measure of ∠C

(i)

C

=

60°
(ii)

C

=

63°
(iii)

C

=

59°
(iv)

C

=

62°
(v)

C

=

61°

Question 21

21.

In △FGH, if ∠F = 30° and ∠G = ∠H, find the measure of each of the equal angles of the triangle

(i)

75°
(ii)

76°
(iii)

74°
(iv)

77°
(v)

73°

Question 22

22.

One angle of a triangle measures 54° and the other two angles are in the ratio 5 : 9. Find these angles.

(i)

B

=

44°

,

C

=

80°
(ii)

B

=

46°

,

C

=

82°
(iii)

B

=

43°

,

C

=

79°
(iv)

B

=

45°

,

C

=

81°
(v)

B

=

47°

,

C

=

83°

Question 23

23.

In a right-angled triangle, the two acute angles are in the ratio 1 : 8. Find these angles.

(i)

A

=

12°

,

C

=

82°
(ii)

A

=

11°

,

C

=

81°
(iii)

A

=

8°

,

C

=

78°
(iv)

A

=

9°

,

C

=

79°
(v)

A

=

10°

,

C

=

80°

Question 24

24.

One of the two equal angles of an isosceles triangle measures 67°. Find the measure of each angle of the triangle.

(i)

A

=

67°

,

B

=

65°

,

C

=

48°
(ii)

A

=

65°

,

B

=

69°

,

C

=

46°
(iii)

A

=

65°

,

B

=

67°

,

C

=

48°
(iv)

A

=

67°

,

B

=

67°

,

C

=

46°
(v)

A

=

69°

,

B

=

67°

,

C

=

44°

Question 25

25.

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

(i)

45°
(ii)

47°
(iii)

46°
(iv)

44°
(v)

43°

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)

59°
(iii)

62°
(iv)

61°
(v)

58°

Question 27

27.

In a right-angled triangle if one of the acute angles is 62°, find the measure of the other acute angle.

(i)

29°
(ii)

28°
(iii)

26°
(iv)

27°
(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

=

118°

,

B

=

30°

,

C

=

32°
(ii)

A

=

120°

,

B

=

30°

,

C

=

30°
(iii)

A

=

122°

,

B

=

30°

,

C

=

28°
(iv)

A

=

120°

,

B

=

28°

,

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

=

20°

,

B

=

80°

,

C

=

80°
(iii)

A

=

18°

,

B

=

82°

,

C

=

80°
(iv)

A

=

18°

,

B

=

80°

,

C

=

82°
(v)

A

=

20°

,

B

=

78°

,

C

=

82°

Question 30

30.

The ratio between the base angle and the vertical angle of an isosceles triangle is 5 : 8. Find each angle of the triangle

(i)

A

=

82°

,

B

=

50°

,

C

=

48°
(ii)

A

=

78°

,

B

=

50°

,

C

=

52°
(iii)

A

=

80°

,

B

=

48°

,

C

=

52°
(iv)

A

=

80°

,

B

=

50°

,

C

=

50°
(v)

A

=

78°

,

B

=

52°

,

C

=

50°

Question 31

31.

In the given figure, find ∠FGE

(i)

64°
(ii)

62°
(iii)

66°
(iv)

63°
(v)

65°

Question 32

32.

In the given figure, find ∠ECD

(i)

100°
(ii)

101°
(iii)

102°
(iv)

103°
(v)

99°

Question 33

33.

In the given figure, find ∠EFD

(i)

47°
(ii)

49°
(iii)

46°
(iv)

48°
(v)

50°

Question 34

34.

In the given figure, find ∠JNM

(i)

137°
(ii)

141°
(iii)

138°
(iv)

139°
(v)

140°

Question 35

35.

In the given figure , if LI ⟂ JK and ∠IJL = 42.82°, find ∠LIJ

(i)

46.18°
(ii)

48.18°
(iii)

49.18°
(iv)

45.18°
(v)

47.18°

Question 36

36.

In the given figure , if FC ⟂ DE and ∠CDF = 50.35°, find ∠ECF

(i)

26.44°
(ii)

24.44°
(iii)

25.44°
(iv)

28.44°
(v)

27.44°

Question 37

37.

In the given figure , if DA ⟂ BC and ∠ABD = 43.63°, find ∠DCA

(i)

57.82°
(ii)

58.82°
(iii)

55.82°
(iv)

59.82°
(v)

56.82°

Question 38

38.

In below given figure, find ∠ADC

(i)

110.70°
(ii)

113.70°
(iii)

109.70°
(iv)

112.70°
(v)

111.70°

Question 39

39.

In below given figure, find ∠MJK

(i)

66.68°
(ii)

67.68°
(iii)

65.68°
(iv)

64.68°
(v)

63.68°

Question 40

40.

In below given figure, find ∠MKO

(i)

91.27°
(ii)

87.27°
(iii)

88.27°
(iv)

89.27°
(v)

90.27°

Question 41

41.

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

(i)

x

=

19.48°

,

y

=

44°
(ii)

x

=

20.48°

,

y

=

45°
(iii)

x

=

22.48°

,

y

=

47°
(iv)

x

=

18.48°

,

y

=

43°
(v)

x

=

21.48°

,

y

=

46°

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

=

90°

,

Z

=

47°
(ii)

X

=

45°

,

Y

=

88°

,

Z

=

47°
(iii)

X

=

47°

,

Y

=

90°

,

Z

=

43°
(iv)

X

=

43°

,

Y

=

92°

,

Z

=

45°
(v)

X

=

45°

,

Y

=

90°

,

Z

=

45°

Question 43

43.

(i)

119°
(ii)

122°
(iii)

121°
(iv)

120°
(v)

118°

Question 44

44.

In the given figure, △BCD is a triangle in which ∠C = 51.14° and ∠D = 63.93°.

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

(i)

120.47°
(ii)

124.47°
(iii)

123.47°
(iv)

122.47°
(v)

121.47°

Question 45

45.

In the given figure, ∠A = 63.07° and ∠B = 51.88°.

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

(i)

x

=

32.52°

,

y

=

57.48°
(ii)

x

=

30.52°

,

y

=

55.48°
(iii)

x

=

34.52°

,

y

=

59.48°
(iv)

x

=

31.52°

,

y

=

56.48°
(v)

x

=

33.52°

,

y

=

58.48°

Question 46

46.

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

(i)

x

=

49.14°

,

y

=

49.41°
(ii)

x

=

50.14°

,

y

=

50.41°
(iii)

x

=

51.14°

,

y

=

51.41°
(iv)

x

=

48.14°

,

y

=

48.41°
(v)

x

=

52.14°

,

y

=

52.41°

Question 47

47.

In the given figure, △GHI in which ∠H = 58.17° and ∠I = 56.08°. GJ and HI bisects each other. Find the value of z

(i)

z

=

66.75°
(ii)

z

=

63.75°
(iii)

z

=

64.75°
(iv)

z

=

65.75°
(v)

z

=

67.75°

Question 48

48.

In the given figure, NO ∥ PQ, ∠GDO = 59° and DE = FD. Find the measure of x.

(i)

x

=

61°
(ii)

x

=

63°
(iii)

x

=

62°
(iv)

x

=

60°
(v)

x

=

64°

Question 49

49.

In the given figure, find the value of x.

(i)

x

=

27.5°
(ii)

x

=

25.5°
(iii)

x

=

26.5°
(iv)

x

=

28.5°
(v)

x

=

29.5°

Question 50

50.

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

(i)

x

=

38°

,

y

=

68°

,

z

=

42°
(ii)

x

=

36°

,

y

=

72°

,

z

=

40°
(iii)

x

=

36°

,

y

=

70°

,

z

=

42°
(iv)

x

=

40°

,

y

=

70°

,

z

=

38°
(v)

x

=

38°

,

y

=

70°

,

z

=

40°

Question 51

51.

In the given figure, if CA = AD = BD. Find the value of x.

(i)

x

=

80°
(ii)

x

=

77°
(iii)

x

=

79°
(iv)

x

=

78°
(v)

x

=

76°

Question 52

52.

In the given figure, if GE = GH = HF, find the value of x

(i)

x

=

19°
(ii)

x

=

22°
(iii)

x

=

18°
(iv)

x

=

21°
(v)

x

=

20°

Question 53

53.

In the given figure, if LI = JL and IM = MK , find the value of x.

(i)

x

=

57.36°
(ii)

x

=

58.36°
(iii)

x

=

55.36°
(iv)

x

=

56.36°
(v)

x

=

54.36°

Question 54

54.

In the given figure, if KN = OK, find the values of x , y , z and t

(i)

x =39.84°, y =23.66°, z =23.63° , t =110.92°
(ii)

x =39.84°, y =23.66°, z =22.63° , t =109.92°
(iii)

x =39.84°, y =25.66°, z =24.63° , t =109.92°
(iv)

x =39.84°, y =23.66°, z =21.63° , t =108.92°
(v)

x =39.84°, y =21.66°, z =20.63° , t =109.92°

Question 55

55.

In the given figure, calculate the value of x.

(i)

x

=

23°
(ii)

x

=

22°
(iii)

x

=

25°
(iv)

x

=

24°
(v)

x

=

21°

Question 56

56.

In the given figure, calculate the value of x.

(i)

x

=

73°
(ii)

x

=

75°
(iii)

x

=

76°
(iv)

x

=

72°
(v)

x

=

74°

Question 57

57.

In the given figure, calculate the value of x.

(i)

x

=

43.08°
(ii)

x

=

45.08°
(iii)

x

=

42.08°
(iv)

x

=

44.08°
(v)

x

=

41.08°

Question 58

58.

Find the unknown marked angles in the following figure

(i)

x

=

108°

,

y

=

37°
(ii)

x

=

107°

,

y

=

36°
(iii)

x

=

109°

,

y

=

38°
(iv)

x

=

110°

,

y

=

39°
(v)

x

=

111°

,

y

=

40°

Question 59

59.

Find the unknown marked angles in the following figure

(i)

x

=

113°

,

y

=

113°
(ii)

x

=

116°

,

y

=

116°
(iii)

x

=

114°

,

y

=

114°
(iv)

x

=

115°

,

y

=

115°
(v)

x

=

112°

,

y

=

112°

Question 60

60.

In the given figure, calculate the value of x.

(i)

x

=

144°
(ii)

x

=

146°
(iii)

x

=

145°
(iv)

x

=

142°
(v)

x

=

143°

Question 61

61.

In the given figure, calculate the value of x.

(i)

x

=

20.5°
(ii)

x

=

23.5°
(iii)

x

=

24.5°
(iv)

x

=

21.5°
(v)

x

=

22.5°

Question 62

62.

Find the unknown marked angles in the following figure

(i)

x

=

114°

,

y

=

147°
(ii)

x

=

115°

,

y

=

148°
(iii)

x

=

118°

,

y

=

151°
(iv)

x

=

116°

,

y

=

149°
(v)

x

=

117°

,

y

=

150°

Question 63

63.

In the following figure DE ∥ GF, find the values of x and y.

(i)

x

=

38°

,

y

=

104°
(ii)

x

=

40°

,

y

=

106°
(iii)

x

=

37°

,

y

=

103°
(iv)

x

=

39°

,

y

=

105°
(v)

x

=

36°

,

y

=

102°

Question 64

64.

Find the unknown marked angles in the following figure

(i)

x

=

86°

,

y

=

112°
(ii)

x

=

87°

,

y

=

113°
(iii)

x

=

89°

,

y

=

115°
(iv)

x

=

88°

,

y

=

114°
(v)

x

=

85°

,

y

=

111°

Question 65

65.

In the given figure, it is given that LK ∥ NM , ∠LNM = 65° and ∠LKJ = 85°. Find the value of x.

(i)

x

=

32°
(ii)

x

=

29°
(iii)

x

=

30°
(iv)

x

=

31°
(v)

x

=

28°

Question 66

66.

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

(i)

x

=

59°

,

y

=

33°

,

z

=

96°
(ii)

x

=

61°

,

y

=

35°

,

z

=

92°
(iii)

x

=

57°

,

y

=

37°

,

z

=

94°
(iv)

x

=

57°

,

y

=

35°

,

z

=

96°
(v)

x

=

59°

,

y

=

35°

,

z

=

94°

Question 67

67.

Find the value of x in the given figure.

(i)

x

=

30°
(ii)

x

=

32°
(iii)

x

=

33°
(iv)

x

=

29°
(v)

x

=

31°

Question 68

68.

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

(i)

x

=

90°

,

y

=

49°

,

z

=

80°
(ii)

x

=

90°

,

y

=

51°

,

z

=

78°
(iii)

x

=

88°

,

y

=

51°

,

z

=

80°
(iv)

x

=

88°

,

y

=

53°

,

z

=

78°
(v)

x

=

92°

,

y

=

51°

,

z

=

76°

Question 69

69.

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

(i)

360°
(ii)

359°
(iii)

362°
(iv)

361°
(v)

358°

Question 70

70.

In a right angled triangle, if one of the angles is 40.24°, find the third angle

(i)

79.76°
(ii)

49.76°
(iii)

54.76°
(iv)

64.76°
(v)

59.76°

Question 71

71.

In a right angled triangle, if one of the angles is 47.12°, find the third angle

(i)

47.88°
(ii)

57.88°
(iii)

72.88°
(iv)

42.88°
(v)

52.88°

Assignment Key