EduSahara™ Assignment
Name : Triangle Angle Properties
Chapter : Lines and Angles
Grade : CBSE Grade IX
License : Non Commercial Use
Question
1
1.
Sum of the interior angles in a triangle is
(i)
185°
(ii)
210°
(iii)
190°
(iv)
180°
(v)
195°
Question
2
2.
Two angles of a triangle measure 64° and 64° respectively. Find the measure of the third angle of the triangle
(i)
50°
(ii)
52°
(iii)
51°
(iv)
53°
(v)
54°
Question
3
3.
The angles of a triangle ABC are in the ratio 11 : 4 : 30. Find the measure of each angle of the triangle
(i)
A
=
44°
,
B
=
14°
,
C
=
122°
(ii)
A
=
42°
,
B
=
18°
,
C
=
120°
(iii)
A
=
44°
,
B
=
16°
,
C
=
120°
(iv)
A
=
42°
,
B
=
16°
,
C
=
122°
(v)
A
=
46°
,
B
=
16°
,
C
=
118°
Question
4
4.
Find the unknown angle from the following figure
(i)
x
=
66.2°
(ii)
x
=
65.2°
(iii)
x
=
63.2°
(iv)
x
=
64.2°
(v)
x
=
67.2°
Question
5
5.
In the given figure, △GHI in which side HI has been produced to J. If ∠IGH = x° , ∠GHI = (8a)° , ∠HIG = (3a)° and ∠GIJ = (15a)°, find the values of a and x.
(i)
a
=
10°
,
x
=
70°
(ii)
a
=
11°
,
x
=
71°
(iii)
a
=
8°
,
x
=
68°
(iv)
a
=
9°
,
x
=
69°
(v)
a
=
12°
,
x
=
72°
Question
6
6.
Find the angles of the triangle
(i)
I
=
43°
,
J
=
37°
,
K
=
100°
(ii)
I
=
45°
,
J
=
35°
,
K
=
100°
(iii)
I
=
43°
,
J
=
35°
,
K
=
102°
(iv)
I
=
45°
,
J
=
33°
,
K
=
102°
(v)
I
=
47°
,
J
=
35°
,
K
=
98°
Question
7
7.
Calculate the value of x in the following figure
(i)
x
=
56.26°
(ii)
x
=
57.26°
(iii)
x
=
58.26°
(iv)
x
=
60.26°
(v)
x
=
59.26°
Question
8
8.
Find the unknown marked angle in the following figure
(i)
x
=
63.42°
(ii)
x
=
61.42°
(iii)
x
=
62.42°
(iv)
x
=
59.42°
(v)
x
=
60.42°
Question
9
9.
Find the unknown angles in the following figure
(i)
G
=
54°
,
H
=
54°
(ii)
G
=
56°
,
H
=
56°
(iii)
G
=
52°
,
H
=
52°
(iv)
G
=
55°
,
H
=
55°
(v)
G
=
53°
,
H
=
53°
Question
10
10.
In the following figure, one side of a triangle has been produced. Find all the angles of the triangle
(i)
G
=
50°
,
H
=
43°
,
I
=
87°
(ii)
G
=
50°
,
H
=
45°
,
I
=
85°
(iii)
G
=
48°
,
H
=
47°
,
I
=
85°
(iv)
G
=
48°
,
H
=
45°
,
I
=
87°
(v)
G
=
52°
,
H
=
45°
,
I
=
83°
Question
11
11.
In the following figure, one side of a triangle has been produced. Find all the angles of the triangle.
(i)
I
=
58°
,
J
=
47°
,
K
=
75°
(ii)
I
=
62°
,
J
=
45°
,
K
=
73°
(iii)
I
=
60°
,
J
=
45°
,
K
=
75°
(iv)
I
=
58°
,
J
=
45°
,
K
=
77°
(v)
I
=
60°
,
J
=
43°
,
K
=
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
=
52°
,
y
=
55°
,
z
=
73°
(ii)
x
=
48°
,
y
=
55°
,
z
=
77°
(iii)
x
=
50°
,
y
=
53°
,
z
=
77°
(iv)
x
=
48°
,
y
=
57°
,
z
=
75°
(v)
x
=
50°
,
y
=
55°
,
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
=
58°
,
y
=
73°
(ii)
x
=
59°
,
y
=
74°
(iii)
x
=
60°
,
y
=
75°
(iv)
x
=
61°
,
y
=
76°
(v)
x
=
62°
,
y
=
77°
Question
14
14.
Calculate the value of the lettered angle in the following figure
(i)
x
=
61.17°
(ii)
x
=
58.17°
(iii)
x
=
60.17°
(iv)
x
=
59.17°
(v)
x
=
62.17°
Question
15
15.
Calculate the value of the lettered angle in the following figure
(i)
x
=
54.11°
(ii)
x
=
53.11°
(iii)
x
=
56.11°
(iv)
x
=
55.11°
(v)
x
=
57.11°
Question
16
16.
In △DEF, if ∠D = 64° and ∠E = 56°, find the measure of ∠F
(i)
F
=
59°
(ii)
F
=
60°
(iii)
F
=
61°
(iv)
F
=
62°
(v)
F
=
58°
Question
17
17.
In △HIJ, if ∠H = 80° and ∠I = ∠J, find the measure of each of the equal angles of the triangle
(i)
52°
(ii)
50°
(iii)
49°
(iv)
48°
(v)
51°
Question
18
18.
One angle of a triangle measures 60° and the other two angles are in the ratio 3 : 5. Find these angles.
(i)
B
=
43°
,
C
=
73°
(ii)
B
=
47°
,
C
=
77°
(iii)
B
=
46°
,
C
=
76°
(iv)
B
=
45°
,
C
=
75°
(v)
B
=
44°
,
C
=
74°
Question
19
19.
In a right-angled triangle, the two acute angles are in the ratio 7 : 2. Find these angles.
(i)
A
=
70°
,
C
=
20°
(ii)
A
=
69°
,
C
=
19°
(iii)
A
=
71°
,
C
=
21°
(iv)
A
=
68°
,
C
=
18°
(v)
A
=
72°
,
C
=
22°
Question
20
20.
One of the two equal angles of an isosceles triangle measures 54°. Find the measure of each angle of the triangle.
(i)
A
=
52°
,
B
=
54°
,
C
=
74°
(ii)
A
=
54°
,
B
=
52°
,
C
=
74°
(iii)
A
=
56°
,
B
=
54°
,
C
=
70°
(iv)
A
=
52°
,
B
=
56°
,
C
=
72°
(v)
A
=
54°
,
B
=
54°
,
C
=
72°
Question
21
21.
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)
61°
(iv)
60°
(v)
62°
Question
22
22.
In a right-angled triangle if one of the acute angles is 41°, find the measure of the other acute angle.
(i)
51°
(ii)
50°
(iii)
48°
(iv)
49°
(v)
47°
Question
23
23.
In the given figure, find ∠FGE
(i)
70°
(ii)
71°
(iii)
72°
(iv)
73°
(v)
69°
Question
24
24.
In the given figure, find ∠GEF
(i)
110°
(ii)
109°
(iii)
106°
(iv)
108°
(v)
107°
Question
25
25.
In the given figure, find ∠LMK
(i)
50°
(ii)
51°
(iii)
54°
(iv)
52°
(v)
53°
Question
26
26.
In the given figure, find ∠FJI
(i)
142°
(ii)
139°
(iii)
141°
(iv)
143°
(v)
140°
Question
27
27.
In the given figure , if JG ⟂ HI and ∠GHJ = 45°, find ∠JGH
(i)
43.00°
(ii)
44.00°
(iii)
46.00°
(iv)
45.00°
(v)
47.00°
Question
28
28.
In the given figure , if KH ⟂ IJ and ∠HIK = 50.96°, find ∠JHK
(i)
25.94°
(ii)
23.94°
(iii)
26.94°
(iv)
27.94°
(v)
24.94°
Question
29
29.
In the given figure , if FC ⟂ DE and ∠CDF = 47.2°, find ∠FEC
(i)
58.95°
(ii)
61.95°
(iii)
62.95°
(iv)
59.95°
(v)
60.95°
Question
30
30.
In below given figure, find ∠ILK
(i)
122.00°
(ii)
123.00°
(iii)
124.00°
(iv)
126.00°
(v)
125.00°
Question
31
31.
In below given figure, find ∠KHI
(i)
60.82°
(ii)
63.82°
(iii)
64.82°
(iv)
61.82°
(v)
62.82°
Question
32
32.
In below given figure, find ∠MKO
(i)
105.91°
(ii)
103.91°
(iii)
107.91°
(iv)
106.91°
(v)
104.91°
Question
33
33.
In the given figure, find the values of x and y.
(i)
x
=
123.97°
,
y
=
61.97°
(ii)
x
=
119.97°
,
y
=
57.97°
(iii)
x
=
122.97°
,
y
=
60.97°
(iv)
x
=
120.97°
,
y
=
58.97°
(v)
x
=
121.97°
,
y
=
59.97°
Question
34
34.
In the given figure,
△CDE
is a triangle in which
∠C
=
∠D
=
∠E
.
This bisectors of
∠D
and
∠E
intersect at
F
.
Find
∠F
=
(i)
121°
(ii)
119°
(iii)
122°
(iv)
118°
(v)
120°
Question
35
35.
In the given figure, △FGH is a triangle in which ∠G = 70.32° and ∠H = 42.13°.
If 'z' is the angle between the bisector of ∠G and ∠H, then find z.
(i)
124.78°
(ii)
122.78°
(iii)
125.78°
(iv)
121.78°
(v)
123.78°
Question
36
36.
In the given figure, ∠G = 68.29° and ∠H = 61.21°.
Side HI is produced to J, so that ∠HIG and ∠GIJ form a linear pair.
If
⟶
IK
and
⟶
IL
are the bisectors of
∠HIG
and
∠GIJ
, find x and y.
(i)
x
=
25.25°
,
y
=
64.75°
(ii)
x
=
23.25°
,
y
=
62.75°
(iii)
x
=
27.25°
,
y
=
66.75°
(iv)
x
=
26.25°
,
y
=
65.75°
(v)
x
=
24.25°
,
y
=
63.75°
Question
37
37.
In the given figure, find the values of x and y
(i)
x
=
52.79°
,
y
=
47.72°
(ii)
x
=
53.79°
,
y
=
48.72°
(iii)
x
=
51.79°
,
y
=
46.72°
(iv)
x
=
50.79°
,
y
=
45.72°
(v)
x
=
49.79°
,
y
=
44.72°
Question
38
38.
In the given figure, △GHI in which ∠H = 63.97° and ∠I = 56°. GJ and HI bisects each other. Find the value of z
(i)
z
=
60.03°
(ii)
z
=
58.03°
(iii)
z
=
62.03°
(iv)
z
=
61.03°
(v)
z
=
59.03°
Question
39
39.
In the given figure, calculate the value of x.
(i)
x
=
25°
(ii)
x
=
24°
(iii)
x
=
27°
(iv)
x
=
26°
(v)
x
=
23°
Question
40
40.
In the given figure, calculate the value of x.
(i)
x
=
73.54°
(ii)
x
=
74.54°
(iii)
x
=
72.54°
(iv)
x
=
76.54°
(v)
x
=
75.54°
Question
41
41.
In the given figure, calculate the value of x.
(i)
x
=
66.29°
(ii)
x
=
68.29°
(iii)
x
=
69.29°
(iv)
x
=
65.29°
(v)
x
=
67.29°
Question
42
42.
In the given figure, calculate the value of x.
(i)
x
=
135°
(ii)
x
=
134°
(iii)
x
=
138°
(iv)
x
=
137°
(v)
x
=
136°
Question
43
43.
Find the unknown marked angles in the following figure
(i)
x
=
102°
,
y
=
143°
(ii)
x
=
106°
,
y
=
147°
(iii)
x
=
103°
,
y
=
144°
(iv)
x
=
104°
,
y
=
145°
(v)
x
=
105°
,
y
=
146°
Question
44
44.
Find the unknown marked angles in the following figure
(i)
x
=
93°
,
y
=
116°
(ii)
x
=
94°
,
y
=
117°
(iii)
x
=
95°
,
y
=
118°
(iv)
x
=
91°
,
y
=
114°
(v)
x
=
92°
,
y
=
115°
Question
45
45.
In the given figure, it is given that IH ∥ KJ , ∠IKJ = 77° and ∠IHG = 74°. Find the value of x.
(i)
x
=
28°
(ii)
x
=
31°
(iii)
x
=
29°
(iv)
x
=
30°
(v)
x
=
27°
Assignment Key
1) (iv)
2) (ii)
3) (iii)
4) (ii)
5) (i)
6) (ii)
7) (iii)
8) (ii)
9) (i)
10) (ii)
11) (iii)
12) (v)
13) (iii)
14) (iii)
15) (iv)
16) (ii)
17) (ii)
18) (iv)
19) (i)
20) (v)
21) (iv)
22) (iv)
23) (ii)
24) (iv)
25) (iv)
26) (iii)
27) (iv)
28) (i)
29) (v)
30) (iii)
31) (v)
32) (i)
33) (v)
34) (v)
35) (v)
36) (i)
37) (iii)
38) (i)
39) (i)
40) (ii)
41) (v)
42) (v)
43) (iv)
44) (i)
45) (iii)
