EduSahara™ Worksheet

Question 1

1.

Two angles of a triangle measure 67° and 56° respectively. Find the measure of the third angle of the triangle

(i)

57°
(ii)

56°
(iii)

55°
(iv)

59°
(v)

58°

Question 2

2.

The angles of a triangle ABC are in the ratio 3 : 8 : 25. Find the measure of each angle of the triangle

(i)

A

=

13°

,

B

=

40°

,

C

=

127°
(ii)

A

=

17°

,

B

=

40°

,

C

=

123°
(iii)

A

=

13°

,

B

=

42°

,

C

=

125°
(iv)

A

=

15°

,

B

=

38°

,

C

=

127°
(v)

A

=

15°

,

B

=

40°

,

C

=

125°

Question 3

3.

Find the unknown angle from the following figure

(i)

x

=

88.15°
(ii)

x

=

84.15°
(iii)

x

=

86.15°
(iv)

x

=

87.15°
(v)

x

=

85.15°

Question 4

4.

In the given figure, △IJK in which side JK has been produced to L. If ∠KIJ = x° , ∠IJK = (7/9a)° , ∠JKI = (5/9a)° and ∠IKL = (13/9a)°, find the values of a and x.

(i)

a

=

89°

,

x

=

59°
(ii)

a

=

91°

,

x

=

61°
(iii)

a

=

88°

,

x

=

58°
(iv)

a

=

90°

,

x

=

60°
(v)

a

=

92°

,

x

=

62°

Question 5

5.

Find the angles of the triangle

(i)

H

=

34°

,

I

=

54°

,

J

=

92°
(ii)

H

=

36°

,

I

=

54°

,

J

=

90°
(iii)

H

=

38°

,

I

=

54°

,

J

=

88°
(iv)

H

=

36°

,

I

=

52°

,

J

=

92°
(v)

H

=

34°

,

I

=

56°

,

J

=

90°

Question 6

6.

Calculate the value of x in the following figure

(i)

x

=

38.11°
(ii)

x

=

37.11°
(iii)

x

=

36.11°
(iv)

x

=

35.11°
(v)

x

=

34.11°

Question 7

7.

Calculate the value of x in the following figure

(i)

x

=

55.06°
(ii)

x

=

56.06°
(iii)

x

=

59.06°
(iv)

x

=

58.06°
(v)

x

=

57.06°

Question 8

8.

Find the unknown marked angle in the following figure

(i)

x

=

68.61°
(ii)

x

=

67.61°
(iii)

x

=

70.61°
(iv)

x

=

66.61°
(v)

x

=

69.61°

Question 9

9.

Find the unknown angles in the following figure

(i)

F

=

35°

,

G

=

35°
(ii)

F

=

34°

,

G

=

34°
(iii)

F

=

32°

,

G

=

32°
(iv)

F

=

31°

,

G

=

31°
(v)

F

=

33°

,

G

=

33°

Question 10

10.

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

(i)

B

=

60°

,

C

=

45°

,

D

=

75°
(ii)

B

=

62°

,

C

=

45°

,

D

=

73°
(iii)

B

=

58°

,

C

=

45°

,

D

=

77°
(iv)

B

=

60°

,

C

=

43°

,

D

=

77°
(v)

B

=

58°

,

C

=

47°

,

D

=

75°

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

=

43°

,

N

=

77°
(ii)

L

=

62°

,

M

=

45°

,

N

=

73°
(iii)

L

=

60°

,

M

=

45°

,

N

=

75°
(iv)

L

=

58°

,

M

=

47°

,

N

=

75°
(v)

L

=

58°

,

M

=

45°

,

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

=

65°

,

z

=

77°
(ii)

x

=

40°

,

y

=

63°

,

z

=

77°
(iii)

x

=

40°

,

y

=

65°

,

z

=

75°
(iv)

x

=

42°

,

y

=

65°

,

z

=

73°
(v)

x

=

38°

,

y

=

67°

,

z

=

75°

Question 13

13.

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

(i)

x

=

51°

,

y

=

111°
(ii)

x

=

48°

,

y

=

108°
(iii)

x

=

50°

,

y

=

110°
(iv)

x

=

52°

,

y

=

112°
(v)

x

=

49°

,

y

=

109°

Question 14

14.

Calculate the value of the lettered angle in the following figure

(i)

x

=

61.17°
(ii)

x

=

59.17°
(iii)

x

=

58.17°
(iv)

x

=

62.17°
(v)

x

=

60.17°

Question 15

15.

In the given triangle, ∠D = 95.66°. Find the measure of ∠E and ∠F

(i)

∠E = ∠F = 40.17°
(ii)

∠E = ∠F = 43.17°
(iii)

∠E = ∠F = 44.17°
(iv)

∠E = ∠F = 42.17°
(v)

∠E = ∠F = 41.17°

Question 16

16.

Find the unknown angle in the following figure

(i)

x

=

51.19°
(ii)

x

=

48.19°
(iii)

x

=

52.19°
(iv)

x

=

49.19°
(v)

x

=

50.19°

Question 17

17.

Find the unknown angle in the following figure

(i)

x

=

90°
(ii)

x

=

88°
(iii)

x

=

91°
(iv)

x

=

92°
(v)

x

=

89°

Question 18

18.

Find the unknown angle in the following figure

(i)

x

=

135°
(ii)

x

=

137°
(iii)

x

=

136°
(iv)

x

=

134°
(v)

x

=

133°

Question 19

19.

In △JKL, if ∠J = 56° and ∠K = 70°, find the measure of ∠L

(i)

L

=

56°
(ii)

L

=

53°
(iii)

L

=

55°
(iv)

L

=

54°
(v)

L

=

52°

Question 20

20.

In △FGH, if ∠F = 60° and ∠G = ∠H, find the measure of each of the equal angles of the triangle

(i)

61°
(ii)

59°
(iii)

60°
(iv)

58°
(v)

62°

Question 21

21.

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

=

47°

,

C

=

83°
(iii)

B

=

45°

,

C

=

81°
(iv)

B

=

46°

,

C

=

82°
(v)

B

=

43°

,

C

=

79°

Question 22

22.

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

=

21°

,

C

=

71°
(iii)

A

=

18°

,

C

=

68°
(iv)

A

=

20°

,

C

=

70°
(v)

A

=

22°

,

C

=

72°

Question 23

23.

One of the two equal angles of an isosceles triangle measures 75°. Find the measure of each angle of the triangle.

(i)

A

=

77°

,

B

=

75°

,

C

=

28°
(ii)

A

=

75°

,

B

=

73°

,

C

=

32°
(iii)

A

=

73°

,

B

=

77°

,

C

=

30°
(iv)

A

=

75°

,

B

=

75°

,

C

=

30°
(v)

A

=

73°

,

B

=

75°

,

C

=

32°

Question 24

24.

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 25

25.

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

(i)

60°
(ii)

61°
(iii)

62°
(iv)

58°
(v)

59°

Question 26

26.

In a right-angled triangle if one of the acute angles is 55°, find the measure of the other acute angle.

(i)

34°
(ii)

36°
(iii)

35°
(iv)

33°
(v)

37°

Question 27

27.

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

=

32°

,

C

=

30°
(ii)

A

=

118°

,

B

=

30°

,

C

=

32°
(iii)

A

=

122°

,

B

=

30°

,

C

=

28°
(iv)

A

=

120°

,

B

=

30°

,

C

=

30°
(v)

A

=

120°

,

B

=

28°

,

C

=

32°

Question 28

28.

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

(i)

A

=

20°

,

B

=

78°

,

C

=

82°
(ii)

A

=

22°

,

B

=

80°

,

C

=

78°
(iii)

A

=

20°

,

B

=

80°

,

C

=

80°
(iv)

A

=

18°

,

B

=

82°

,

C

=

80°
(v)

A

=

18°

,

B

=

80°

,

C

=

82°

Question 29

29.

The ratio between the base angle and the vertical angle of an isosceles triangle is 11 : 14. Find each angle of the triangle

(i)

A

=

72°

,

B

=

55°

,

C

=

53°
(ii)

A

=

70°

,

B

=

53°

,

C

=

57°
(iii)

A

=

68°

,

B

=

57°

,

C

=

55°
(iv)

A

=

70°

,

B

=

55°

,

C

=

55°
(v)

A

=

68°

,

B

=

55°

,

C

=

57°

Question 30

30.

In the given figure, find ∠JKI

(i)

53°
(ii)

52°
(iii)

50°
(iv)

51°
(v)

49°

Question 31

31.

In the given figure, find ∠FDE

(i)

121°
(ii)

122°
(iii)

118°
(iv)

119°
(v)

120°

Question 32

32.

In the given figure, find ∠GHF

(i)

37°
(ii)

35°
(iii)

39°
(iv)

38°
(v)

36°

Question 33

33.

In the given figure, find ∠AED

(i)

143°
(ii)

144°
(iii)

140°
(iv)

142°
(v)

141°

Question 34

34.

In the given figure , if GD ⟂ EF and ∠DEG = 60.21°, find ∠GDE

(i)

31.79°
(ii)

30.79°
(iii)

28.79°
(iv)

27.79°
(v)

29.79°

Question 35

35.

In the given figure , if LI ⟂ JK and ∠IJL = 47.73°, find ∠KIL

(i)

30.61°
(ii)

29.61°
(iii)

28.61°
(iv)

26.61°
(v)

27.61°

Question 36

36.

In the given figure , if HE ⟂ FG and ∠EFH = 47.2°, find ∠HGE

(i)

58.95°
(ii)

60.95°
(iii)

59.95°
(iv)

62.95°
(v)

61.95°

Question 37

37.

In below given figure, find ∠GJI

(i)

142.30°
(ii)

139.30°
(iii)

141.30°
(iv)

140.30°
(v)

138.30°

Question 38

38.

In below given figure, find ∠DAB

(i)

63.54°
(ii)

62.54°
(iii)

64.54°
(iv)

65.54°
(v)

61.54°

Question 39

39.

In below given figure, find ∠DBF

(i)

89.63°
(ii)

88.63°
(iii)

86.63°
(iv)

90.63°
(v)

87.63°

Question 40

40.

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

(i)

x

=

26.17°

,

y

=

81.97°
(ii)

x

=

28.17°

,

y

=

83.97°
(iii)

x

=

25.17°

,

y

=

80.97°
(iv)

x

=

24.17°

,

y

=

79.97°
(v)

x

=

27.17°

,

y

=

82.97°

Question 41

41.

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

(i)

X

=

47°

,

Y

=

90°

,

Z

=

43°
(ii)

X

=

45°

,

Y

=

90°

,

Z

=

45°
(iii)

X

=

45°

,

Y

=

88°

,

Z

=

47°
(iv)

X

=

43°

,

Y

=

92°

,

Z

=

45°
(v)

X

=

43°

,

Y

=

90°

,

Z

=

47°

Question 42

42.

In the given figure, find the value of x.

(i)

x

=

127°
(ii)

x

=

124°
(iii)

x

=

126°
(iv)

x

=

125°
(v)

x

=

123°

Question 43

43.

In the given figure, if EC = EF = FD, find the value of x

(i)

x

=

27°
(ii)

x

=

30°
(iii)

x

=

28°
(iv)

x

=

29°
(v)

x

=

26°

Question 44

44.

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

(i)

x

=

68°
(ii)

x

=

67°
(iii)

x

=

69°
(iv)

x

=

66°
(v)

x

=

70°

Question 45

45.

Find the unknown marked angles in the following figure

(i)

x

=

110°

,

y

=

39°
(ii)

x

=

111°

,

y

=

40°
(iii)

x

=

108°

,

y

=

37°
(iv)

x

=

107°

,

y

=

36°
(v)

x

=

109°

,

y

=

38°

Question 46

46.

Find the unknown marked angles in the following figure

(i)

x

=

105°

,

y

=

105°
(ii)

x

=

106°

,

y

=

106°
(iii)

x

=

109°

,

y

=

109°
(iv)

x

=

108°

,

y

=

108°
(v)

x

=

107°

,

y

=

107°

Question 47

47.

Find the unknown marked angles in the following figure

(i)

x

=

102°

,

y

=

152°
(ii)

x

=

101°

,

y

=

151°
(iii)

x

=

98°

,

y

=

148°
(iv)

x

=

99°

,

y

=

149°
(v)

x

=

100°

,

y

=

150°

Question 48

48.

Find the unknown marked angles in the following figure

(i)

x

=

91°

,

y

=

115°
(ii)

x

=

90°

,

y

=

114°
(iii)

x

=

93°

,

y

=

117°
(iv)

x

=

94°

,

y

=

118°
(v)

x

=

92°

,

y

=

116°

Assignment Key