EduSahara™ Assignment
Name : Triangle Angle Properties
Chapter : Lines and Angles
Grade : SSC Grade IX
License : Non Commercial Use
Question
1
1.
In △ABC, if ∠A = 65° and ∠B = 61°, find the measure of ∠C
(i)
C
=
56°
(ii)
C
=
52°
(iii)
C
=
54°
(iv)
C
=
55°
(v)
C
=
53°
Question
2
2.
In △JKL, if ∠J = 70° and ∠K = ∠L, find the measure of each of the equal angles of the triangle
(i)
54°
(ii)
56°
(iii)
55°
(iv)
57°
(v)
53°
Question
3
3.
One angle of a triangle measures 60° and the other two angles are in the ratio 3 : 5. Find these angles.
(i)
B
=
45°
,
C
=
75°
(ii)
B
=
47°
,
C
=
77°
(iii)
B
=
44°
,
C
=
74°
(iv)
B
=
43°
,
C
=
73°
(v)
B
=
46°
,
C
=
76°
Question
4
4.
In a right-angled triangle, the two acute angles are in the ratio 7 : 11. Find these angles.
(i)
A
=
34°
,
C
=
54°
(ii)
A
=
36°
,
C
=
56°
(iii)
A
=
37°
,
C
=
57°
(iv)
A
=
35°
,
C
=
55°
(v)
A
=
33°
,
C
=
53°
Question
5
5.
One of the two equal angles of an isosceles triangle measures 48°. Find the measure of each angle of the triangle.
(i)
A
=
46°
,
B
=
48°
,
C
=
86°
(ii)
A
=
48°
,
B
=
46°
,
C
=
86°
(iii)
A
=
48°
,
B
=
48°
,
C
=
84°
(iv)
A
=
50°
,
B
=
48°
,
C
=
82°
(v)
A
=
46°
,
B
=
50°
,
C
=
84°
Question
6
6.
Find the measure of each of the two equal angles of an isosceles right-angled triangle.
(i)
43°
(ii)
47°
(iii)
45°
(iv)
46°
(v)
44°
Question
7
7.
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)
59°
(iv)
60°
(v)
62°
Question
8
8.
In a right-angled triangle if one of the acute angles is 33°, find the measure of the other acute angle.
(i)
58°
(ii)
55°
(iii)
56°
(iv)
57°
(v)
59°
Question
9
9.
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
=
118°
,
B
=
30°
,
C
=
32°
(iv)
A
=
118°
,
B
=
32°
,
C
=
30°
(v)
A
=
120°
,
B
=
28°
,
C
=
32°
Question
10
10.
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
=
18°
,
B
=
82°
,
C
=
80°
(iv)
A
=
20°
,
B
=
78°
,
C
=
82°
(v)
A
=
18°
,
B
=
80°
,
C
=
82°
Question
11
11.
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
=
52°
,
B
=
65°
,
C
=
63°
(ii)
A
=
48°
,
B
=
67°
,
C
=
65°
(iii)
A
=
50°
,
B
=
63°
,
C
=
67°
(iv)
A
=
48°
,
B
=
65°
,
C
=
67°
(v)
A
=
50°
,
B
=
65°
,
C
=
65°
Question
12
12.
In the given figure, find the values of x and y.
(i)
x
=
20.88°
,
y
=
52.99°
(ii)
x
=
22.88°
,
y
=
54.99°
(iii)
x
=
19.88°
,
y
=
51.99°
(iv)
x
=
21.88°
,
y
=
53.99°
(v)
x
=
23.88°
,
y
=
55.99°
Question
13
13.
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
=
45°
,
Y
=
88°
,
Z
=
47°
(iii)
X
=
47°
,
Y
=
90°
,
Z
=
43°
(iv)
X
=
43°
,
Y
=
92°
,
Z
=
45°
(v)
X
=
43°
,
Y
=
90°
,
Z
=
47°
Question
14
14.
In the given figure,
△GHI
is a triangle in which
∠G
=
∠H
=
∠I
.
This bisectors of
∠H
and
∠I
intersect at
J
.
Find
∠J
=
(i)
120°
(ii)
118°
(iii)
122°
(iv)
121°
(v)
119°
Question
15
15.
In the given figure, △HIJ is a triangle in which ∠I = 51.76° and ∠J = 68°.
If 'z' is the angle between the bisector of ∠I and ∠J, then find z.
(i)
119.12°
(ii)
120.12°
(iii)
121.12°
(iv)
118.12°
(v)
122.12°
Question
16
16.
In the given figure, ∠M = 50.06° and ∠N = 68.15°.
Side NO is produced to P, so that ∠NOM and ∠MOP form a linear pair.
If
⟶
OQ
and
⟶
OR
are the bisectors of
∠NOM
and
∠MOP
, find x and y.
(i)
x
=
29.89°
,
y
=
58.11°
(ii)
x
=
28.89°
,
y
=
57.11°
(iii)
x
=
30.89°
,
y
=
59.11°
(iv)
x
=
32.89°
,
y
=
61.11°
(v)
x
=
31.89°
,
y
=
60.11°
Question
17
17.
In the given figure, find the values of x and y
(i)
x
=
59.07°
,
y
=
48.24°
(ii)
x
=
63.07°
,
y
=
52.24°
(iii)
x
=
60.07°
,
y
=
49.24°
(iv)
x
=
62.07°
,
y
=
51.24°
(v)
x
=
61.07°
,
y
=
50.24°
Question
18
18.
In the given figure, △EFG in which ∠F = 53.72° and ∠G = 57.29°. EH and FG bisects each other. Find the value of z
(i)
z
=
67.99°
(ii)
z
=
66.99°
(iii)
z
=
68.99°
(iv)
z
=
69.99°
(v)
z
=
70.99°
Question
19
19.
In the given figure, PQ ∥ RS, ∠IFQ = 56° and FG = HF. Find the measure of x.
(i)
x
=
66°
(ii)
x
=
67°
(iii)
x
=
68°
(iv)
x
=
70°
(v)
x
=
69°
Question
20
20.
In the given figure, find the value of x.
(i)
x
=
133°
(ii)
x
=
131°
(iii)
x
=
130°
(iv)
x
=
132°
(v)
x
=
129°
Question
21
21.
In the given figure, JK ∥ LM and JL = LN. Find the values of x,y and z.
(i)
x
=
30°
,
y
=
70°
,
z
=
44°
(ii)
x
=
30°
,
y
=
68°
,
z
=
46°
(iii)
x
=
32°
,
y
=
66°
,
z
=
46°
(iv)
x
=
34°
,
y
=
68°
,
z
=
42°
(v)
x
=
32°
,
y
=
68°
,
z
=
44°
Question
22
22.
In the given figure, if HF = FI = GI. Find the value of x.
(i)
x
=
97.5°
(ii)
x
=
95.5°
(iii)
x
=
99.5°
(iv)
x
=
96.5°
(v)
x
=
98.5°
Question
23
23.
In the given figure, if HF = HI = IG, find the value of x
(i)
x
=
18°
(ii)
x
=
21°
(iii)
x
=
19°
(iv)
x
=
20°
(v)
x
=
22°
Question
24
24.
In the given figure, if MJ = KM and JN = NL , find the value of x.
(i)
x
=
56.38°
(ii)
x
=
54.38°
(iii)
x
=
57.38°
(iv)
x
=
55.38°
(v)
x
=
53.38°
Question
25
25.
In the given figure, if MP = QM, find the values of x , y , z and t
(i)
x =42.28°, y =24.59°, z =23.71° , t =111.14°
(ii)
x =42.28°, y =22.59°, z =21.71° , t =111.14°
(iii)
x =42.28°, y =26.59°, z =25.71° , t =111.14°
(iv)
x =42.28°, y =24.59°, z =24.71° , t =112.14°
(v)
x =42.28°, y =24.59°, z =22.71° , t =110.14°
Question
26
26.
In the given figure, calculate the value of x.
(i)
x
=
27°
(ii)
x
=
26°
(iii)
x
=
25°
(iv)
x
=
24°
(v)
x
=
23°
Question
27
27.
In the given figure, calculate the value of x.
(i)
x
=
75.45°
(ii)
x
=
74.45°
(iii)
x
=
71.45°
(iv)
x
=
72.45°
(v)
x
=
73.45°
Question
28
28.
In the given figure, calculate the value of x.
(i)
x
=
42.62°
(ii)
x
=
43.62°
(iii)
x
=
45.62°
(iv)
x
=
44.62°
(v)
x
=
41.62°
Question
29
29.
Find the unknown marked angles in the following figure
(i)
x
=
111°
,
y
=
44°
(ii)
x
=
113°
,
y
=
46°
(iii)
x
=
115°
,
y
=
48°
(iv)
x
=
112°
,
y
=
45°
(v)
x
=
114°
,
y
=
47°
Question
30
30.
Find the unknown marked angles in the following figure
(i)
x
=
113°
,
y
=
113°
(ii)
x
=
115°
,
y
=
115°
(iii)
x
=
111°
,
y
=
111°
(iv)
x
=
114°
,
y
=
114°
(v)
x
=
112°
,
y
=
112°
Question
31
31.
In the given figure, calculate the value of x.
(i)
x
=
139°
(ii)
x
=
136°
(iii)
x
=
140°
(iv)
x
=
138°
(v)
x
=
137°
Question
32
32.
In the given figure, calculate the value of x.
(i)
x
=
21.5°
(ii)
x
=
20.5°
(iii)
x
=
23.5°
(iv)
x
=
24.5°
(v)
x
=
22.5°
Question
33
33.
Find the unknown marked angles in the following figure
(i)
x
=
106°
,
y
=
143°
(ii)
x
=
107°
,
y
=
144°
(iii)
x
=
109°
,
y
=
146°
(iv)
x
=
110°
,
y
=
147°
(v)
x
=
108°
,
y
=
145°
Question
34
34.
In the following figure CD ∥ FE, find the values of x and y.
(i)
x
=
30°
,
y
=
126°
(ii)
x
=
26°
,
y
=
122°
(iii)
x
=
29°
,
y
=
125°
(iv)
x
=
28°
,
y
=
124°
(v)
x
=
27°
,
y
=
123°
Question
35
35.
Find the unknown marked angles in the following figure
(i)
x
=
89°
,
y
=
112°
(ii)
x
=
91°
,
y
=
114°
(iii)
x
=
90°
,
y
=
113°
(iv)
x
=
93°
,
y
=
116°
(v)
x
=
92°
,
y
=
115°
Question
36
36.
In the given figure, it is given that FE ∥ HG , ∠FHG = 77° and ∠FED = 75°. Find the value of x.
(i)
x
=
30°
(ii)
x
=
26°
(iii)
x
=
29°
(iv)
x
=
28°
(v)
x
=
27°
Question
37
37.
In the given figure, find the values of x ,y and z.
(i)
x
=
33°
,
y
=
37°
,
z
=
70°
(ii)
x
=
37°
,
y
=
35°
,
z
=
68°
(iii)
x
=
33°
,
y
=
35°
,
z
=
72°
(iv)
x
=
35°
,
y
=
33°
,
z
=
72°
(v)
x
=
35°
,
y
=
35°
,
z
=
70°
Question
38
38.
Find the value of x in the given figure.
(i)
x
=
29°
(ii)
x
=
32°
(iii)
x
=
31°
(iv)
x
=
33°
(v)
x
=
30°
Question
39
39.
In the given figure, find the values of x ,y and z.
(i)
x
=
80°
,
y
=
63°
,
z
=
56°
(ii)
x
=
84°
,
y
=
63°
,
z
=
52°
(iii)
x
=
82°
,
y
=
63°
,
z
=
54°
(iv)
x
=
82°
,
y
=
61°
,
z
=
56°
(v)
x
=
80°
,
y
=
65°
,
z
=
54°
Assignment Key
1) (iii)
2) (iii)
3) (i)
4) (iv)
5) (iii)
6) (iii)
7) (iv)
8) (iv)
9) (ii)
10) (ii)
11) (v)
12) (iv)
13) (i)
14) (i)
15) (ii)
16) (iii)
17) (v)
18) (iii)
19) (iii)
20) (ii)
21) (v)
22) (i)
23) (iv)
24) (iv)
25) (i)
26) (iii)
27) (v)
28) (ii)
29) (ii)
30) (i)
31) (iv)
32) (v)
33) (v)
34) (iv)
35) (ii)
36) (iv)
37) (v)
38) (iii)
39) (iii)
