EduSahara™ Assignment
Name : Triangle Angle Properties
Chapter : Triangles
Grade : ICSE Grade VII
License : Non Commercial Use
Question
1
1.
Two angles of a triangle measure 69° and 60° respectively. Find the measure of the third angle of the triangle
(i)
49°
(ii)
51°
(iii)
50°
(iv)
52°
(v)
53°
Question
2
2.
The angles of a triangle ABC are in the ratio 4 : 3 : 5. Find the measure of each angle of the triangle
(i)
A
=
60°
,
B
=
43°
,
C
=
77°
(ii)
A
=
60°
,
B
=
45°
,
C
=
75°
(iii)
A
=
58°
,
B
=
45°
,
C
=
77°
(iv)
A
=
58°
,
B
=
47°
,
C
=
75°
(v)
A
=
62°
,
B
=
45°
,
C
=
73°
Question
3
3.
Find the unknown angle from the following figure
(i)
x
=
39.71°
(ii)
x
=
43.71°
(iii)
x
=
40.71°
(iv)
x
=
41.71°
(v)
x
=
42.71°
Question
4
4.
In the given figure, △IJK in which side JK has been produced to L. If ∠KIJ = x° , ∠IJK = (2a)° , ∠JKI = (1a)° and ∠IKL = (5a)°, find the values of a and x.
(i)
a
=
32°
,
x
=
92°
(ii)
a
=
31°
,
x
=
91°
(iii)
a
=
29°
,
x
=
89°
(iv)
a
=
30°
,
x
=
90°
(v)
a
=
28°
,
x
=
88°
Question
5
5.
Find the angles of the triangle
(i)
A
=
58°
,
B
=
25°
,
C
=
97°
(ii)
A
=
60°
,
B
=
25°
,
C
=
95°
(iii)
A
=
62°
,
B
=
25°
,
C
=
93°
(iv)
A
=
58°
,
B
=
27°
,
C
=
95°
(v)
A
=
60°
,
B
=
23°
,
C
=
97°
Question
6
6.
Calculate the value of x in the following figure
(i)
x
=
66.67°
(ii)
x
=
67.67°
(iii)
x
=
64.67°
(iv)
x
=
65.67°
(v)
x
=
63.67°
Question
7
7.
Calculate the value of x in the following figure
(i)
x
=
88.46°
(ii)
x
=
85.46°
(iii)
x
=
89.46°
(iv)
x
=
87.46°
(v)
x
=
86.46°
Question
8
8.
Find the unknown marked angle in the following figure
(i)
x
=
50.56°
(ii)
x
=
46.56°
(iii)
x
=
47.56°
(iv)
x
=
48.56°
(v)
x
=
49.56°
Question
9
9.
Find the unknown angles in the following figure
(i)
J
=
60°
,
K
=
60°
(ii)
J
=
58°
,
K
=
58°
(iii)
J
=
59°
,
K
=
59°
(iv)
J
=
57°
,
K
=
57°
(v)
J
=
61°
,
K
=
61°
Question
10
10.
In the following figure, one side of a triangle has been produced. Find all the angles of the triangle
(i)
F
=
52°
,
G
=
20°
,
H
=
108°
(ii)
F
=
48°
,
G
=
22°
,
H
=
110°
(iii)
F
=
50°
,
G
=
20°
,
H
=
110°
(iv)
F
=
48°
,
G
=
20°
,
H
=
112°
(v)
F
=
50°
,
G
=
18°
,
H
=
112°
Question
11
11.
In the following figure, one side of a triangle has been produced. Find all the angles of the triangle.
(i)
G
=
28°
,
H
=
55°
,
I
=
97°
(ii)
G
=
32°
,
H
=
55°
,
I
=
93°
(iii)
G
=
28°
,
H
=
57°
,
I
=
95°
(iv)
G
=
30°
,
H
=
55°
,
I
=
95°
(v)
G
=
30°
,
H
=
53°
,
I
=
97°
Question
12
12.
In the following figure, two sides of a triangle have been produced. Find all the angles of the triangle.
(i)
x
=
18°
,
y
=
32°
,
z
=
130°
(ii)
x
=
20°
,
y
=
30°
,
z
=
130°
(iii)
x
=
22°
,
y
=
30°
,
z
=
128°
(iv)
x
=
20°
,
y
=
28°
,
z
=
132°
(v)
x
=
18°
,
y
=
30°
,
z
=
132°
Question
13
13.
In the following figure, one side of a triangle has been produced. Find the values of x and y.
(i)
x
=
25°
,
y
=
85°
(ii)
x
=
24°
,
y
=
84°
(iii)
x
=
23°
,
y
=
83°
(iv)
x
=
27°
,
y
=
87°
(v)
x
=
26°
,
y
=
86°
Question
14
14.
Calculate the value of the lettered angle in the following figure
(i)
x
=
39.03°
(ii)
x
=
38.03°
(iii)
x
=
42.03°
(iv)
x
=
40.03°
(v)
x
=
41.03°
Question
15
15.
Calculate the value of the lettered angle in the following figure
(i)
x
=
45°
(ii)
x
=
47°
(iii)
x
=
46°
(iv)
x
=
44°
(v)
x
=
43°
Question
16
16.
In the given triangle, ∠E = 53.96°. Find the measure of ∠F and ∠G
(i)
∠F = ∠G = 62.02°
(ii)
∠F = ∠G = 61.02°
(iii)
∠F = ∠G = 64.02°
(iv)
∠F = ∠G = 63.02°
(v)
∠F = ∠G = 65.02°
Question
17
17.
Find the unknown angle in the following figure
(i)
x
=
62.13°
(ii)
x
=
61.13°
(iii)
x
=
58.13°
(iv)
x
=
59.13°
(v)
x
=
60.13°
Question
18
18.
Find the unknown angle in the following figure
(i)
x
=
43°
(ii)
x
=
44°
(iii)
x
=
46°
(iv)
x
=
47°
(v)
x
=
45°
Question
19
19.
Find the unknown angle in the following figure
(i)
x
=
137°
(ii)
x
=
135°
(iii)
x
=
136°
(iv)
x
=
133°
(v)
x
=
134°
Question
20
20.
In △FGH, if ∠F = 56° and ∠G = 57°, find the measure of ∠H
(i)
H
=
68°
(ii)
H
=
67°
(iii)
H
=
66°
(iv)
H
=
65°
(v)
H
=
69°
Question
21
21.
In △ABC, if ∠A = 90° and ∠B = ∠C, find the measure of each of the equal angles of the triangle
(i)
46°
(ii)
43°
(iii)
47°
(iv)
45°
(v)
44°
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
=
45°
,
C
=
81°
(ii)
B
=
43°
,
C
=
79°
(iii)
B
=
46°
,
C
=
82°
(iv)
B
=
47°
,
C
=
83°
(v)
B
=
44°
,
C
=
80°
Question
23
23.
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
=
25°
,
C
=
65°
(iii)
A
=
23°
,
C
=
63°
(iv)
A
=
24°
,
C
=
64°
(v)
A
=
26°
,
C
=
66°
Question
24
24.
One of the two equal angles of an isosceles triangle measures 70°. Find the measure of each angle of the triangle.
(i)
A
=
72°
,
B
=
70°
,
C
=
38°
(ii)
A
=
70°
,
B
=
70°
,
C
=
40°
(iii)
A
=
68°
,
B
=
72°
,
C
=
40°
(iv)
A
=
68°
,
B
=
70°
,
C
=
42°
(v)
A
=
70°
,
B
=
68°
,
C
=
42°
Question
25
25.
Find the measure of each of the two equal angles of an isosceles right-angled triangle.
(i)
46°
(ii)
47°
(iii)
43°
(iv)
44°
(v)
45°
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)
58°
(ii)
61°
(iii)
62°
(iv)
60°
(v)
59°
Question
27
27.
In a right-angled triangle if one of the acute angles is 52°, find the measure of the other acute angle.
(i)
36°
(ii)
37°
(iii)
40°
(iv)
38°
(v)
39°
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
=
122°
,
B
=
30°
,
C
=
28°
(ii)
A
=
120°
,
B
=
30°
,
C
=
30°
(iii)
A
=
120°
,
B
=
28°
,
C
=
32°
(iv)
A
=
118°
,
B
=
30°
,
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
=
18°
,
B
=
80°
,
C
=
82°
(ii)
A
=
22°
,
B
=
80°
,
C
=
78°
(iii)
A
=
20°
,
B
=
80°
,
C
=
80°
(iv)
A
=
20°
,
B
=
78°
,
C
=
82°
(v)
A
=
18°
,
B
=
82°
,
C
=
80°
Question
30
30.
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
=
70°
,
B
=
55°
,
C
=
55°
(iv)
A
=
68°
,
B
=
57°
,
C
=
55°
(v)
A
=
68°
,
B
=
55°
,
C
=
57°
Question
31
31.
In the given figure, find ∠EFD
(i)
73°
(ii)
77°
(iii)
74°
(iv)
76°
(v)
75°
Question
32
32.
In the given figure, find ∠JHI
(i)
119°
(ii)
121°
(iii)
122°
(iv)
123°
(v)
120°
Question
33
33.
In the given figure, find ∠JKI
(i)
46°
(ii)
45°
(iii)
44°
(iv)
47°
(v)
43°
Question
34
34.
In the given figure, find ∠KON
(i)
154°
(ii)
152°
(iii)
150°
(iv)
151°
(v)
153°
Question
35
35.
In the given figure , if LI ⟂ JK and ∠IJL = 41.13°, find ∠LIJ
(i)
47.87°
(ii)
48.87°
(iii)
49.87°
(iv)
50.87°
(v)
46.87°
Question
36
36.
In the given figure , if KH ⟂ IJ and ∠HIK = 46.31°, find ∠JHK
(i)
27.82°
(ii)
30.82°
(iii)
29.82°
(iv)
28.82°
(v)
31.82°
Question
37
37.
In the given figure , if DA ⟂ BC and ∠ABD = 41.13°, find ∠DCA
(i)
53.51°
(ii)
57.51°
(iii)
54.51°
(iv)
55.51°
(v)
56.51°
Question
38
38.
In below given figure, find ∠BED
(i)
120.05°
(ii)
118.05°
(iii)
119.05°
(iv)
117.05°
(v)
116.05°
Question
39
39.
In below given figure, find ∠DAB
(i)
60.60°
(ii)
59.60°
(iii)
57.60°
(iv)
58.60°
(v)
61.60°
Question
40
40.
In below given figure, find ∠FDH
(i)
100.69°
(ii)
98.69°
(iii)
102.69°
(iv)
101.69°
(v)
99.69°
Question
41
41.
In the given figure, find the values of x and y.
(i)
x
=
22.41°
,
y
=
43.35°
(ii)
x
=
20.41°
,
y
=
41.35°
(iii)
x
=
21.41°
,
y
=
42.35°
(iv)
x
=
18.41°
,
y
=
39.35°
(v)
x
=
19.41°
,
y
=
40.35°
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
=
90°
,
Z
=
45°
(ii)
X
=
43°
,
Y
=
90°
,
Z
=
47°
(iii)
X
=
43°
,
Y
=
92°
,
Z
=
45°
(iv)
X
=
47°
,
Y
=
90°
,
Z
=
43°
(v)
X
=
45°
,
Y
=
88°
,
Z
=
47°
Question
43
43.
In the given figure, find the values of x and y
(i)
x
=
66.04°
,
y
=
44.71°
(ii)
x
=
67.04°
,
y
=
45.71°
(iii)
x
=
65.04°
,
y
=
43.71°
(iv)
x
=
68.04°
,
y
=
46.71°
(v)
x
=
69.04°
,
y
=
47.71°
Question
44
44.
In the given figure, PQ ∥ RS, ∠EBQ = 61° and BC = DB. Find the measure of x.
(i)
x
=
58°
(ii)
x
=
56°
(iii)
x
=
60°
(iv)
x
=
57°
(v)
x
=
59°
Question
45
45.
In the given figure, find the value of x.
(i)
x
=
24.5°
(ii)
x
=
22.5°
(iii)
x
=
25.5°
(iv)
x
=
21.5°
(v)
x
=
23.5°
Question
46
46.
In the given figure, BC ∥ DE and BD = DF. Find the values of x,y and z.
(i)
x
=
30°
,
y
=
68°
,
z
=
48°
(ii)
x
=
32°
,
y
=
64°
,
z
=
50°
(iii)
x
=
32°
,
y
=
66°
,
z
=
48°
(iv)
x
=
34°
,
y
=
66°
,
z
=
46°
(v)
x
=
30°
,
y
=
66°
,
z
=
50°
Question
47
47.
In the given figure, if IG = GJ = HJ. Find the value of x.
(i)
x
=
70°
(ii)
x
=
69°
(iii)
x
=
68°
(iv)
x
=
71°
(v)
x
=
67°
Question
48
48.
In the given figure, if CA = CD = DB, find the value of x
(i)
x
=
34°
(ii)
x
=
38°
(iii)
x
=
35°
(iv)
x
=
36°
(v)
x
=
37°
Question
49
49.
In the given figure, if KH = IK and HL = LJ , find the value of x.
(i)
x
=
59.06°
(ii)
x
=
61.06°
(iii)
x
=
60.06°
(iv)
x
=
58.06°
(v)
x
=
57.06°
Question
50
50.
In the given figure, if DG = HD, find the values of x , y , z and t
(i)
x =57.76°, y =26.23°, z =26.38° , t =119.88°
(ii)
x =57.76°, y =24.23°, z =23.38° , t =118.88°
(iii)
x =57.76°, y =26.23°, z =24.38° , t =117.88°
(iv)
x =57.76°, y =28.23°, z =27.38° , t =118.88°
(v)
x =57.76°, y =26.23°, z =25.38° , t =118.88°
Question
51
51.
In the given figure, calculate the value of x.
(i)
x
=
24°
(ii)
x
=
23°
(iii)
x
=
21°
(iv)
x
=
20°
(v)
x
=
22°
Question
52
52.
In the given figure, calculate the value of x.
(i)
x
=
72.24°
(ii)
x
=
69.24°
(iii)
x
=
71.24°
(iv)
x
=
70.24°
(v)
x
=
73.24°
Question
53
53.
In the given figure, calculate the value of x.
(i)
x
=
41.37°
(ii)
x
=
37.37°
(iii)
x
=
40.37°
(iv)
x
=
38.37°
(v)
x
=
39.37°
Question
54
54.
Find the unknown marked angles in the following figure
(i)
x
=
112°
,
y
=
44°
(ii)
x
=
110°
,
y
=
42°
(iii)
x
=
113°
,
y
=
45°
(iv)
x
=
111°
,
y
=
43°
(v)
x
=
114°
,
y
=
46°
Question
55
55.
Find the unknown marked angles in the following figure
(i)
x
=
111°
,
y
=
111°
(ii)
x
=
112°
,
y
=
112°
(iii)
x
=
113°
,
y
=
113°
(iv)
x
=
115°
,
y
=
115°
(v)
x
=
114°
,
y
=
114°
Question
56
56.
In the given figure, calculate the value of x.
(i)
x
=
130°
(ii)
x
=
131°
(iii)
x
=
133°
(iv)
x
=
134°
(v)
x
=
132°
Question
57
57.
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
58
58.
Find the unknown marked angles in the following figure
(i)
x
=
109°
,
y
=
153°
(ii)
x
=
108°
,
y
=
152°
(iii)
x
=
107°
,
y
=
151°
(iv)
x
=
110°
,
y
=
154°
(v)
x
=
106°
,
y
=
150°
Question
59
59.
In the following figure IJ ∥ LK, find the values of x and y.
(i)
x
=
31°
,
y
=
121°
(ii)
x
=
28°
,
y
=
118°
(iii)
x
=
30°
,
y
=
120°
(iv)
x
=
29°
,
y
=
119°
(v)
x
=
32°
,
y
=
122°
Question
60
60.
In the given figure, it is given that HG ∥ JI , ∠HJI = 65° and ∠HGF = 86°. Find the value of x.
(i)
x
=
28°
(ii)
x
=
27°
(iii)
x
=
31°
(iv)
x
=
30°
(v)
x
=
29°
Question
61
61.
In the given two equilateral triangles, find ∠M + ∠O + ∠Q + ∠N + ∠P + ∠R .
(i)
361°
(ii)
360°
(iii)
362°
(iv)
358°
(v)
359°
Assignment Key
1) (ii)
2) (ii)
3) (iv)
4) (iv)
5) (ii)
6) (iv)
7) (iv)
8) (iv)
9) (iii)
10) (iii)
11) (iv)
12) (ii)
13) (i)
14) (iv)
15) (i)
16) (iv)
17) (v)
18) (v)
19) (ii)
20) (ii)
21) (iv)
22) (i)
23) (ii)
24) (ii)
25) (v)
26) (iv)
27) (iv)
28) (ii)
29) (iii)
30) (iii)
31) (v)
32) (ii)
33) (ii)
34) (ii)
35) (ii)
36) (iii)
37) (iv)
38) (ii)
39) (ii)
40) (i)
41) (ii)
42) (i)
43) (ii)
44) (i)
45) (v)
46) (iii)
47) (ii)
48) (iv)
49) (i)
50) (v)
51) (v)
52) (iii)
53) (v)
54) (i)
55) (iii)
56) (v)
57) (v)
58) (ii)
59) (iii)
60) (v)
61) (ii)
