EduSahara™ Worksheet

Question 1

1.

Two angles of a triangle measure 55° and 57° respectively. Find the measure of the third angle of the triangle

(i)

66°
(ii)

67°
(iii)

69°
(iv)

68°
(v)

70°

Question 2

2.

The angles of a triangle ABC are in the ratio 3 : 2 : 7. Find the measure of each angle of the triangle

(i)

A

=

43°

,

B

=

30°

,

C

=

107°
(ii)

A

=

45°

,

B

=

30°

,

C

=

105°
(iii)

A

=

43°

,

B

=

32°

,

C

=

105°
(iv)

A

=

45°

,

B

=

28°

,

C

=

107°
(v)

A

=

47°

,

B

=

30°

,

C

=

103°

Question 3

3.

Find the unknown angle from the following figure

(i)

x

=

52.93°
(ii)

x

=

50.93°
(iii)

x

=

48.93°
(iv)

x

=

51.93°
(v)

x

=

49.93°

Question 4

4.

In the given figure, △IJK in which side JK has been produced to L. If ∠KIJ = x° , ∠IJK = (5/12a)° , ∠JKI = (1/4a)° and ∠IKL = (5/4a)°, find the values of a and x.

(i)

a

=

120°

,

x

=

100°
(ii)

a

=

122°

,

x

=

102°
(iii)

a

=

119°

,

x

=

99°
(iv)

a

=

121°

,

x

=

101°
(v)

a

=

118°

,

x

=

98°

Question 5

5.

Find the angles of the triangle

(i)

A

=

25°

,

B

=

40°

,

C

=

115°
(ii)

A

=

25°

,

B

=

38°

,

C

=

117°
(iii)

A

=

27°

,

B

=

40°

,

C

=

113°
(iv)

A

=

23°

,

B

=

42°

,

C

=

115°
(v)

A

=

23°

,

B

=

40°

,

C

=

117°

Question 6

6.

Calculate the value of x in the following figure

(i)

x

=

92.47°
(ii)

x

=

94.47°
(iii)

x

=

91.47°
(iv)

x

=

93.47°
(v)

x

=

95.47°

Question 7

7.

Calculate the value of x in the following figure

(i)

x

=

44.78°
(ii)

x

=

43.78°
(iii)

x

=

45.78°
(iv)

x

=

41.78°
(v)

x

=

42.78°

Question 8

8.

Find the unknown marked angle in the following figure

(i)

x

=

60.21°
(ii)

x

=

61.21°
(iii)

x

=

58.21°
(iv)

x

=

62.21°
(v)

x

=

59.21°

Question 9

9.

Find the unknown angles in the following figure

(i)

F

=

38°

,

G

=

38°
(ii)

F

=

37°

,

G

=

37°
(iii)

F

=

36°

,

G

=

36°
(iv)

F

=

39°

,

G

=

39°
(v)

F

=

40°

,

G

=

40°

Question 10

10.

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

(i)

K

=

45°

,

L

=

34°

,

M

=

101°
(ii)

K

=

43°

,

L

=

38°

,

M

=

99°
(iii)

K

=

47°

,

L

=

36°

,

M

=

97°
(iv)

K

=

45°

,

L

=

36°

,

M

=

99°
(v)

K

=

43°

,

L

=

36°

,

M

=

101°

Question 11

11.

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

(i)

I

=

62°

,

J

=

45°

,

K

=

73°
(ii)

I

=

60°

,

J

=

43°

,

K

=

77°
(iii)

I

=

58°

,

J

=

45°

,

K

=

77°
(iv)

I

=

60°

,

J

=

45°

,

K

=

75°
(v)

I

=

58°

,

J

=

47°

,

K

=

75°

Question 12

12.

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

(i)

x

=

62°

,

y

=

45°

,

z

=

73°
(ii)

x

=

60°

,

y

=

43°

,

z

=

77°
(iii)

x

=

60°

,

y

=

45°

,

z

=

75°
(iv)

x

=

58°

,

y

=

47°

,

z

=

75°
(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

=

27°

,

y

=

127°
(ii)

x

=

23°

,

y

=

123°
(iii)

x

=

26°

,

y

=

126°
(iv)

x

=

25°

,

y

=

125°
(v)

x

=

24°

,

y

=

124°

Question 14

14.

Identify the property by which the two given triangles are congruent

(i)

SSS Congruency
(ii)

SAS Congruency
(iii)

ASA Congruency
(iv)

RHS Congruency

Question 15

15.

Identify the property by which the two given triangles are congruent

(i)

RHS Congruency
(ii)

SSS Congruency
(iii)

ASA Congruency
(iv)

SAS Congruency

Question 16

16.

Identify the property by which the two given triangles are congruent

(i)

SAS Congruency
(ii)

ASA Congruency
(iii)

RHS Congruency
(iv)

SSS Congruency

Question 17

17.

Identify the property by which the two given triangles are congruent

(i)

ASA Congruency
(ii)

RHS Congruency
(iii)

SSS Congruency
(iv)

SAS Congruency

Question 18

18.

Calculate the value of the lettered angle in the following figure

(i)

x

=

59.17°
(ii)

x

=

60.17°
(iii)

x

=

58.17°
(iv)

x

=

62.17°
(v)

x

=

61.17°

Question 19

19.

Calculate the value of the lettered angle in the following figure

(i)

x

=

35.84°
(ii)

x

=

34.84°
(iii)

x

=

32.84°
(iv)

x

=

36.84°
(v)

x

=

33.84°

Question 20

20.

In the given triangle, ∠A = 92.06°. Find the measure of ∠B and ∠C

(i)

∠B = ∠C = 42.97°
(ii)

∠B = ∠C = 43.97°
(iii)

∠B = ∠C = 44.97°
(iv)

∠B = ∠C = 41.97°
(v)

∠B = ∠C = 45.97°

Question 21

21.

Find the unknown angle in the following figure

(i)

x

=

37.87°
(ii)

x

=

38.87°
(iii)

x

=

41.87°
(iv)

x

=

39.87°
(v)

x

=

40.87°

Question 22

22.

Find the unknown angle in the following figure

(i)

x

=

47°
(ii)

x

=

44°
(iii)

x

=

45°
(iv)

x

=

46°
(v)

x

=

43°

Question 23

23.

Find the unknown angle in the following figure

(i)

x

=

134°
(ii)

x

=

135°
(iii)

x

=

133°
(iv)

x

=

137°
(v)

x

=

136°

Question 24

24.

In △CDE, if ∠C = 67° and ∠D = 69°, find the measure of ∠E

(i)

E

=

45°
(ii)

E

=

46°
(iii)

E

=

42°
(iv)

E

=

44°
(v)

E

=

43°

Question 25

25.

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

(i)

75°
(ii)

77°
(iii)

76°
(iv)

74°
(v)

73°

Question 26

26.

One angle of a triangle measures 35° and the other two angles are in the ratio 6 : 23. Find these angles.

(i)

B

=

29°

,

C

=

114°
(ii)

B

=

28°

,

C

=

113°
(iii)

B

=

32°

,

C

=

117°
(iv)

B

=

30°

,

C

=

115°
(v)

B

=

31°

,

C

=

116°

Question 27

27.

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

(i)

A

=

27°

,

C

=

67°
(ii)

A

=

23°

,

C

=

63°
(iii)

A

=

24°

,

C

=

64°
(iv)

A

=

25°

,

C

=

65°
(v)

A

=

26°

,

C

=

66°

Question 28

28.

One of the two equal angles of an isosceles triangle measures 73°. Find the measure of each angle of the triangle.

(i)

A

=

71°

,

B

=

75°

,

C

=

34°
(ii)

A

=

75°

,

B

=

73°

,

C

=

32°
(iii)

A

=

73°

,

B

=

71°

,

C

=

36°
(iv)

A

=

71°

,

B

=

73°

,

C

=

36°
(v)

A

=

73°

,

B

=

73°

,

C

=

34°

Question 29

29.

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

(i)

46°
(ii)

44°
(iii)

45°
(iv)

43°
(v)

47°

Question 30

30.

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

(i)

59°
(ii)

62°
(iii)

60°
(iv)

58°
(v)

61°

Question 31

31.

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

(i)

30°
(ii)

29°
(iii)

32°
(iv)

31°
(v)

33°

Question 32

32.

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

=

122°

,

B

=

30°

,

C

=

28°
(v)

A

=

118°

,

B

=

30°

,

C

=

32°

Question 33

33.

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

=

20°

,

B

=

80°

,

C

=

80°
(iii)

A

=

18°

,

B

=

80°

,

C

=

82°
(iv)

A

=

18°

,

B

=

82°

,

C

=

80°
(v)

A

=

22°

,

B

=

80°

,

C

=

78°

Question 34

34.

The ratio between the base angle and the vertical angle of an isosceles triangle is 13 : 10. Find each angle of the triangle

(i)

A

=

48°

,

B

=

67°

,

C

=

65°
(ii)

A

=

50°

,

B

=

63°

,

C

=

67°
(iii)

A

=

48°

,

B

=

65°

,

C

=

67°
(iv)

A

=

52°

,

B

=

65°

,

C

=

63°
(v)

A

=

50°

,

B

=

65°

,

C

=

65°

Question 35

35.

In the given figure, find ∠FGE

(i)

60°
(ii)

63°
(iii)

61°
(iv)

62°
(v)

64°

Question 36

36.

In the given figure, find ∠MKL

(i)

108°
(ii)

112°
(iii)

110°
(iv)

111°
(v)

109°

Question 37

37.

In the given figure, find ∠NOM

(i)

47°
(ii)

46°
(iii)

48°
(iv)

49°
(v)

50°

Question 38

38.

In the given figure, find ∠BFE

(i)

129°
(ii)

128°
(iii)

131°
(iv)

127°
(v)

130°

Question 39

39.

In the given figure , if HE ⟂ FG and ∠EFH = 42.82°, find ∠HEF

(i)

48.18°
(ii)

46.18°
(iii)

49.18°
(iv)

45.18°
(v)

47.18°

Question 40

40.

In the given figure , if DA ⟂ BC and ∠ABD = 50.35°, find ∠CAD

(i)

28.44°
(ii)

25.44°
(iii)

24.44°
(iv)

26.44°
(v)

27.44°

Question 41

41.

In the given figure , if HE ⟂ FG and ∠EFH = 57.99°, find ∠HGE

(i)

69.44°
(ii)

67.44°
(iii)

70.44°
(iv)

68.44°
(v)

71.44°

Question 42

42.

In below given figure, find ∠CFE

(i)

130.93°
(ii)

134.93°
(iii)

133.93°
(iv)

131.93°
(v)

132.93°

Question 43

43.

In below given figure, find ∠FCD

(i)

55.73°
(ii)

56.73°
(iii)

54.73°
(iv)

57.73°
(v)

58.73°

Question 44

44.

In below given figure, find ∠CAE

(i)

99.40°
(ii)

98.40°
(iii)

101.40°
(iv)

97.40°
(v)

100.40°

Question 45

45.

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

(i)

x

=

42.47°

,

y

=

56.28°
(ii)

x

=

41.47°

,

y

=

55.28°
(iii)

x

=

43.47°

,

y

=

57.28°
(iv)

x

=

40.47°

,

y

=

54.28°
(v)

x

=

39.47°

,

y

=

53.28°

Question 46

46.

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

=

45°

,

Y

=

88°

,

Z

=

47°
(iv)

X

=

43°

,

Y

=

92°

,

Z

=

45°
(v)

X

=

47°

,

Y

=

90°

,

Z

=

43°

Question 47

47.

(i)

119°
(ii)

118°
(iii)

121°
(iv)

120°
(v)

122°

Question 48

48.

In the given figure, △DEF is a triangle in which ∠E = 47.04° and ∠F = 50.19°.

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

(i)

133.38°
(ii)

130.38°
(iii)

131.38°
(iv)

132.38°
(v)

129.38°

Question 49

49.

In the given figure, ∠A = 53.01° and ∠B = 68.09°.

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

(i)

x

=

28.45°

,

y

=

59.55°
(ii)

x

=

29.45°

,

y

=

60.55°
(iii)

x

=

27.45°

,

y

=

58.55°
(iv)

x

=

31.45°

,

y

=

62.55°
(v)

x

=

30.45°

,

y

=

61.55°

Question 50

50.

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

(i)

x

=

63.77°

,

y

=

45.01°
(ii)

x

=

65.77°

,

y

=

47.01°
(iii)

x

=

64.77°

,

y

=

46.01°
(iv)

x

=

67.77°

,

y

=

49.01°
(v)

x

=

66.77°

,

y

=

48.01°

Question 51

51.

In the given figure, △BCD in which ∠C = 55.3° and ∠D = 65.23°. BE and CD bisects each other. Find the value of z

(i)

z

=

59.47°
(ii)

z

=

57.47°
(iii)

z

=

61.47°
(iv)

z

=

58.47°
(v)

z

=

60.47°

Question 52

52.

In the given figure, QR ∥ ST, ∠JGR = 64° and GH = IG. Find the measure of x.

(i)

x

=

50°
(ii)

x

=

53°
(iii)

x

=

52°
(iv)

x

=

51°
(v)

x

=

54°

Question 53

53.

In the given figure, find the value of x.

(i)

x

=

28°
(ii)

x

=

26°
(iii)

x

=

29°
(iv)

x

=

27°
(v)

x

=

25°

Question 54

54.

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

(i)

x

=

33°

,

y

=

74°

,

z

=

36°
(ii)

x

=

35°

,

y

=

72°

,

z

=

36°
(iii)

x

=

37°

,

y

=

72°

,

z

=

34°
(iv)

x

=

33°

,

y

=

72°

,

z

=

38°
(v)

x

=

35°

,

y

=

70°

,

z

=

38°

Question 55

55.

In the given figure, if EC = CF = DF. Find the value of x.

(i)

x

=

74°
(ii)

x

=

73°
(iii)

x

=

76°
(iv)

x

=

75°
(v)

x

=

77°

Question 56

56.

In the given figure, if CA = CD = DB, find the value of x

(i)

x

=

23°
(ii)

x

=

26°
(iii)

x

=

25°
(iv)

x

=

22°
(v)

x

=

24°

Question 57

57.

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

(i)

x

=

59.64°
(ii)

x

=

57.64°
(iii)

x

=

58.64°
(iv)

x

=

56.64°
(v)

x

=

55.64°

Question 58

58.

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

(i)

x =59.58°, y =28.85°, z =27.2° , t =119.79°
(ii)

x =59.58°, y =26.85°, z =25.2° , t =119.79°
(iii)

x =59.58°, y =26.85°, z =24.2° , t =118.79°
(iv)

x =59.58°, y =24.85°, z =23.2° , t =119.79°
(v)

x =59.58°, y =26.85°, z =26.2° , t =120.79°

Question 59

59.

In the given figure, calculate the value of x.

(i)

x

=

21°
(ii)

x

=

19°
(iii)

x

=

20°
(iv)

x

=

18°
(v)

x

=

22°

Question 60

60.

In the given figure, calculate the value of x.

(i)

x

=

71.82°
(ii)

x

=

69.82°
(iii)

x

=

68.82°
(iv)

x

=

72.82°
(v)

x

=

70.82°

Question 61

61.

In the given figure, calculate the value of x.

(i)

x

=

72.8°
(ii)

x

=

71.8°
(iii)

x

=

73.8°
(iv)

x

=

75.8°
(v)

x

=

74.8°

Question 62

62.

Find the unknown marked angles in the following figure

(i)

x

=

109°

,

y

=

39°
(ii)

x

=

108°

,

y

=

38°
(iii)

x

=

112°

,

y

=

42°
(iv)

x

=

110°

,

y

=

40°
(v)

x

=

111°

,

y

=

41°

Question 63

63.

Find the unknown marked angles in the following figure

(i)

x

=

106°

,

y

=

106°
(ii)

x

=

105°

,

y

=

105°
(iii)

x

=

107°

,

y

=

107°
(iv)

x

=

108°

,

y

=

108°
(v)

x

=

109°

,

y

=

109°

Question 64

64.

In the given figure, calculate the value of x.

(i)

x

=

139°
(ii)

x

=

138°
(iii)

x

=

140°
(iv)

x

=

141°
(v)

x

=

142°

Question 65

65.

In the given figure, calculate the value of x.

(i)

x

=

21.5°
(ii)

x

=

23.5°
(iii)

x

=

24.5°
(iv)

x

=

20.5°
(v)

x

=

22.5°

Question 66

66.

Find the unknown marked angles in the following figure

(i)

x

=

113°

,

y

=

149°
(ii)

x

=

110°

,

y

=

146°
(iii)

x

=

112°

,

y

=

148°
(iv)

x

=

111°

,

y

=

147°
(v)

x

=

109°

,

y

=

145°

Question 67

67.

In the following figure IJ ∥ LK, find the values of x and y.

(i)

x

=

56°

,

y

=

68°
(ii)

x

=

54°

,

y

=

66°
(iii)

x

=

55°

,

y

=

67°
(iv)

x

=

57°

,

y

=

69°
(v)

x

=

58°

,

y

=

70°

Question 68

68.

Find the unknown marked angles in the following figure

(i)

x

=

96°

,

y

=

120°
(ii)

x

=

93°

,

y

=

117°
(iii)

x

=

94°

,

y

=

118°
(iv)

x

=

97°

,

y

=

121°
(v)

x

=

95°

,

y

=

119°

Question 69

69.

In the given figure, it is given that ED ∥ GF , ∠EGF = 74° and ∠EDC = 81°. Find the value of x.

(i)

x

=

25°
(ii)

x

=

26°
(iii)

x

=

24°
(iv)

x

=

27°
(v)

x

=

23°

Question 70

70.

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

(i)

x

=

43°

,

y

=

37°

,

z

=

84°
(ii)

x

=

43°

,

y

=

39°

,

z

=

82°
(iii)

x

=

45°

,

y

=

37°

,

z

=

82°
(iv)

x

=

45°

,

y

=

35°

,

z

=

84°
(v)

x

=

47°

,

y

=

37°

,

z

=

80°

Question 71

71.

Find the value of x in the given figure.

(i)

x

=

22°
(ii)

x

=

26°
(iii)

x

=

24°
(iv)

x

=

25°
(v)

x

=

23°

Question 72

72.

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

(i)

x

=

90°

,

y

=

62°

,

z

=

54°
(ii)

x

=

88°

,

y

=

66°

,

z

=

52°
(iii)

x

=

88°

,

y

=

64°

,

z

=

54°
(iv)

x

=

92°

,

y

=

64°

,

z

=

50°
(v)

x

=

90°

,

y

=

64°

,

z

=

52°

Question 73

73.

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

(i)

358°
(ii)

361°
(iii)

360°
(iv)

359°
(v)

362°

Assignment Key