EduSahara™ Worksheet

Question 1

1.

Two angles of a triangle measure 60° and 61° respectively. Find the measure of the third angle of the triangle

(i)

57°
(ii)

59°
(iii)

60°
(iv)

58°
(v)

61°

Question 2

2.

The angles of a triangle ABC are in the ratio 6 : 3 : 9. Find the measure of each angle of the triangle

(i)

A

=

58°

,

B

=

32°

,

C

=

90°
(ii)

A

=

60°

,

B

=

30°

,

C

=

90°
(iii)

A

=

62°

,

B

=

30°

,

C

=

88°
(iv)

A

=

60°

,

B

=

28°

,

C

=

92°
(v)

A

=

58°

,

B

=

30°

,

C

=

92°

Question 3

3.

Find the unknown angle from the following figure

(i)

x

=

53.28°
(ii)

x

=

51.28°
(iii)

x

=

49.28°
(iv)

x

=

50.28°
(v)

x

=

52.28°

Question 4

4.

In the given figure, △CDE in which side DE has been produced to F. If ∠ECD = x° , ∠CDE = (1/4a)° , ∠DEC = (1/4a)° and ∠CEF = (5/4a)°, find the values of a and x.

(i)

a

=

121°

,

x

=

121°
(ii)

a

=

118°

,

x

=

118°
(iii)

a

=

119°

,

x

=

119°
(iv)

a

=

122°

,

x

=

122°
(v)

a

=

120°

,

x

=

120°

Question 5

5.

Find the angles of the triangle

(i)

D

=

34°

,

E

=

63°

,

F

=

83°
(ii)

D

=

34°

,

E

=

65°

,

F

=

81°
(iii)

D

=

36°

,

E

=

63°

,

F

=

81°
(iv)

D

=

38°

,

E

=

63°

,

F

=

79°
(v)

D

=

36°

,

E

=

61°

,

F

=

83°

Question 6

6.

Calculate the value of x in the following figure

(i)

x

=

60.18°
(ii)

x

=

57.18°
(iii)

x

=

59.18°
(iv)

x

=

56.18°
(v)

x

=

58.18°

Question 7

7.

Calculate the value of x in the following figure

(i)

x

=

59.36°
(ii)

x

=

60.36°
(iii)

x

=

61.36°
(iv)

x

=

62.36°
(v)

x

=

58.36°

Question 8

8.

Find the unknown marked angle in the following figure

(i)

x

=

63.07°
(ii)

x

=

64.07°
(iii)

x

=

66.07°
(iv)

x

=

62.07°
(v)

x

=

65.07°

Question 9

9.

Find the unknown angles in the following figure

(i)

B

=

46°

,

C

=

46°
(ii)

B

=

47°

,

C

=

47°
(iii)

B

=

43°

,

C

=

43°
(iv)

B

=

45°

,

C

=

45°
(v)

B

=

44°

,

C

=

44°

Question 10

10.

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

(i)

K

=

58°

,

L

=

47°

,

M

=

75°
(ii)

K

=

60°

,

L

=

45°

,

M

=

75°
(iii)

K

=

58°

,

L

=

45°

,

M

=

77°
(iv)

K

=

62°

,

L

=

45°

,

M

=

73°
(v)

K

=

60°

,

L

=

43°

,

M

=

77°

Question 11

11.

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

(i)

M

=

30°

,

N

=

18°

,

O

=

132°
(ii)

M

=

32°

,

N

=

20°

,

O

=

128°
(iii)

M

=

28°

,

N

=

20°

,

O

=

132°
(iv)

M

=

30°

,

N

=

20°

,

O

=

130°
(v)

M

=

28°

,

N

=

22°

,

O

=

130°

Question 12

12.

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

(i)

x

=

56°

,

y

=

45°

,

z

=

79°
(ii)

x

=

54°

,

y

=

43°

,

z

=

83°
(iii)

x

=

54°

,

y

=

45°

,

z

=

81°
(iv)

x

=

52°

,

y

=

45°

,

z

=

83°
(v)

x

=

52°

,

y

=

47°

,

z

=

81°

Question 13

13.

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

(i)

x

=

60°

,

y

=

75°
(ii)

x

=

61°

,

y

=

76°
(iii)

x

=

62°

,

y

=

77°
(iv)

x

=

58°

,

y

=

73°
(v)

x

=

59°

,

y

=

74°

Question 14

14.

Calculate the value of the lettered angle in the following figure

(i)

x

=

47.34°
(ii)

x

=

43.34°
(iii)

x

=

46.34°
(iv)

x

=

45.34°
(v)

x

=

44.34°

Question 15

15.

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

(i)

∠J = ∠K = 56.13°
(ii)

∠J = ∠K = 55.13°
(iii)

∠J = ∠K = 54.13°
(iv)

∠J = ∠K = 57.13°
(v)

∠J = ∠K = 53.13°

Question 16

16.

Find the unknown angle in the following figure

(i)

x

=

60.95°
(ii)

x

=

61.95°
(iii)

x

=

59.95°
(iv)

x

=

58.95°
(v)

x

=

62.95°

Question 17

17.

Find the unknown angle in the following figure

(i)

x

=

88°
(ii)

x

=

91°
(iii)

x

=

92°
(iv)

x

=

90°
(v)

x

=

89°

Question 18

18.

Find the unknown angle in the following figure

(i)

x

=

133°
(ii)

x

=

136°
(iii)

x

=

137°
(iv)

x

=

134°
(v)

x

=

135°

Question 19

19.

In △IJK, if ∠I = 51° and ∠J = 51°, find the measure of ∠K

(i)

K

=

76°
(ii)

K

=

78°
(iii)

K

=

77°
(iv)

K

=

80°
(v)

K

=

79°

Question 20

20.

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

(i)

54°
(ii)

53°
(iii)

56°
(iv)

55°
(v)

57°

Question 21

21.

One angle of a triangle measures 55° and the other two angles are in the ratio 4 : 21. Find these angles.

(i)

B

=

20°

,

C

=

105°
(ii)

B

=

21°

,

C

=

106°
(iii)

B

=

22°

,

C

=

107°
(iv)

B

=

19°

,

C

=

104°
(v)

B

=

18°

,

C

=

103°

Question 22

22.

In a right-angled triangle, the two acute angles are in the ratio 5 : 4. Find these angles.

(i)

A

=

51°

,

C

=

41°
(ii)

A

=

52°

,

C

=

42°
(iii)

A

=

50°

,

C

=

40°
(iv)

A

=

48°

,

C

=

38°
(v)

A

=

49°

,

C

=

39°

Question 23

23.

One of the two equal angles of an isosceles triangle measures 56°. Find the measure of each angle of the triangle.

(i)

A

=

54°

,

B

=

58°

,

C

=

68°
(ii)

A

=

58°

,

B

=

56°

,

C

=

66°
(iii)

A

=

54°

,

B

=

56°

,

C

=

70°
(iv)

A

=

56°

,

B

=

56°

,

C

=

68°
(v)

A

=

56°

,

B

=

54°

,

C

=

70°

Question 24

24.

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

(i)

43°
(ii)

44°
(iii)

46°
(iv)

47°
(v)

45°

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)

58°
(ii)

59°
(iii)

60°
(iv)

61°
(v)

62°

Question 26

26.

In a right-angled triangle if one of the acute angles is 43°, find the measure of the other acute angle.

(i)

46°
(ii)

48°
(iii)

49°
(iv)

45°
(v)

47°

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

=

120°

,

B

=

30°

,

C

=

30°
(ii)

A

=

122°

,

B

=

30°

,

C

=

28°
(iii)

A

=

120°

,

B

=

28°

,

C

=

32°
(iv)

A

=

118°

,

B

=

30°

,

C

=

32°
(v)

A

=

118°

,

B

=

32°

,

C

=

30°

Question 28

28.

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

=

20°

,

B

=

78°

,

C

=

82°
(iv)

A

=

18°

,

B

=

80°

,

C

=

82°
(v)

A

=

18°

,

B

=

82°

,

C

=

80°

Question 29

29.

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

=

58°

,

C

=

62°
(ii)

A

=

58°

,

B

=

60°

,

C

=

62°
(iii)

A

=

62°

,

B

=

60°

,

C

=

58°
(iv)

A

=

60°

,

B

=

60°

,

C

=

60°
(v)

A

=

58°

,

B

=

62°

,

C

=

60°

Question 30

30.

In the given figure, find ∠IJH

(i)

79°
(ii)

75°
(iii)

77°
(iv)

76°
(v)

78°

Question 31

31.

In the given figure, find ∠KIJ

(i)

114°
(ii)

110°
(iii)

112°
(iv)

111°
(v)

113°

Question 32

32.

In the given figure, find ∠KLJ

(i)

53°
(ii)

49°
(iii)

52°
(iv)

50°
(v)

51°

Question 33

33.

In the given figure, find ∠DHG

(i)

143°
(ii)

145°
(iii)

144°
(iv)

147°
(v)

146°

Question 34

34.

In the given figure , if GD ⟂ EF and ∠DEG = 53.94°, find ∠GDE

(i)

37.06°
(ii)

36.06°
(iii)

34.06°
(iv)

38.06°
(v)

35.06°

Question 35

35.

In the given figure , if JG ⟂ HI and ∠GHJ = 50.35°, find ∠IGJ

(i)

28.44°
(ii)

25.44°
(iii)

26.44°
(iv)

27.44°
(v)

24.44°

Question 36

36.

In the given figure , if GD ⟂ EF and ∠DEG = 43.63°, find ∠GFD

(i)

56.82°
(ii)

55.82°
(iii)

59.82°
(iv)

57.82°
(v)

58.82°

Question 37

37.

In below given figure, find ∠ADC

(i)

128.07°
(ii)

126.07°
(iii)

125.07°
(iv)

127.07°
(v)

124.07°

Question 38

38.

In below given figure, find ∠NKL

(i)

50.81°
(ii)

51.81°
(iii)

53.81°
(iv)

49.81°
(v)

52.81°

Question 39

39.

In below given figure, find ∠HFJ

(i)

83.43°
(ii)

87.43°
(iii)

85.43°
(iv)

86.43°
(v)

84.43°

Question 40

40.

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

(i)

x

=

26.83°

,

y

=

51.97°
(ii)

x

=

25.83°

,

y

=

50.97°
(iii)

x

=

29.83°

,

y

=

54.97°
(iv)

x

=

27.83°

,

y

=

52.97°
(v)

x

=

28.83°

,

y

=

53.97°

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

=

43°

,

Y

=

90°

,

Z

=

47°
(ii)

X

=

45°

,

Y

=

90°

,

Z

=

45°
(iii)

X

=

43°

,

Y

=

92°

,

Z

=

45°
(iv)

X

=

45°

,

Y

=

88°

,

Z

=

47°
(v)

X

=

47°

,

Y

=

90°

,

Z

=

43°

Question 42

42.

In the given figure, find the value of x.

(i)

x

=

24°
(ii)

x

=

28°
(iii)

x

=

27°
(iv)

x

=

25°
(v)

x

=

26°

Question 43

43.

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

(i)

x

=

41°
(ii)

x

=

38°
(iii)

x

=

40°
(iv)

x

=

39°
(v)

x

=

42°

Question 44

44.

In the given figure, if EB = CE and BF = FD , find the value of x.

(i)

x

=

63°
(ii)

x

=

64°
(iii)

x

=

66°
(iv)

x

=

65°
(v)

x

=

62°

Question 45

45.

Find the unknown marked angles in the following figure

(i)

x

=

106°

,

y

=

31°
(ii)

x

=

107°

,

y

=

32°
(iii)

x

=

103°

,

y

=

28°
(iv)

x

=

105°

,

y

=

30°
(v)

x

=

104°

,

y

=

29°

Question 46

46.

Find the unknown marked angles in the following figure

(i)

x

=

112°

,

y

=

112°
(ii)

x

=

114°

,

y

=

114°
(iii)

x

=

111°

,

y

=

111°
(iv)

x

=

110°

,

y

=

110°
(v)

x

=

113°

,

y

=

113°

Question 47

47.

Find the unknown marked angles in the following figure

(i)

x

=

109°

,

y

=

150°
(ii)

x

=

108°

,

y

=

149°
(iii)

x

=

107°

,

y

=

148°
(iv)

x

=

110°

,

y

=

151°
(v)

x

=

111°

,

y

=

152°

Question 48

48.

Find the unknown marked angles in the following figure

(i)

x

=

89°

,

y

=

115°
(ii)

x

=

87°

,

y

=

113°
(iii)

x

=

88°

,

y

=

114°
(iv)

x

=

85°

,

y

=

111°
(v)

x

=

86°

,

y

=

112°

Assignment Key