EduSahara™ Assignment
Name : Angle Computation
Chapter : Quadrilaterals
Grade : SSC Grade IX
License : Non Commercial Use
Question
1
1.
Find the missing angle in the given quadrilateral
(i)
72.27°
(ii)
57.27°
(iii)
62.27°
(iv)
67.27°
(v)
87.27°
Question
2
2.
Find the missing angle in the given trapezium
(i)
104.18°
(ii)
134.18°
(iii)
109.18°
(iv)
119.18°
(v)
114.18°
Question
3
3.
Find the missing angle in the given parallelogram
(i)
87.26°
(ii)
82.26°
(iii)
77.26°
(iv)
92.26°
(v)
107.26°
Question
4
4.
Find the missing angle in the given rhombus
(i)
112.28°
(ii)
122.28°
(iii)
142.28°
(iv)
127.28°
(v)
117.28°
Question
5
5.
The measures of three angles of a quadrilateral are
54.07°
,
136.66°
and
43.28°
. Find the fourth angle
(i)
140.99°
(ii)
130.99°
(iii)
125.99°
(iv)
135.99°
(v)
155.99°
Question
6
6.
Sum of the interior angles in a quadrilateral is
(i)
360°
(ii)
370°
(iii)
375°
(iv)
365°
(v)
390°
Question
7
7.
In parallelogram ABCD, if ∠A = 66.98°, then find the value of ∠B
(i)
111.02°
(ii)
114.02°
(iii)
113.02°
(iv)
112.02°
(v)
115.02°
Question
8
8.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
92°
(ii)
88°
(iii)
91°
(iv)
90°
(v)
89°
Question
9
9.
If ABCD is an isosceles trapezium, ∠D =
(i)
∠A
(ii)
∠B
(iii)
90°
(iv)
∠C
Question
10
10.
DEFG is a rhombus in which ∠D = 120° .
EG
is the diagonal. Then △DEF is
(i)
None of these
(ii)
an obtuse angled triangle
(iii)
an equilateral triangle
(iv)
an isosceles triangle
(v)
a scalene triangle
Question
11
11.
JKLM is a rhombus in which ∠J = 85° .
KM
is the diagonal. Then △JKL is
(i)
a scalene triangle
(ii)
None of these
(iii)
an obtuse angled triangle
(iv)
an isosceles triangle
(v)
an equilateral triangle
Question
12
12.
The angles of a quadrilateral MNOP are in the ratio 4 : 5 : 6 : 9. Find the measure of each angle of the quadrilateral.
(i)
M
=
60°
,
N
=
75°
,
O
=
90°
,
P
=
135°
(ii)
M
=
62°
,
N
=
74°
,
O
=
88°
,
P
=
136°
(iii)
M
=
58°
,
N
=
77°
,
O
=
89°
,
P
=
136°
(iv)
M
=
61°
,
N
=
74°
,
O
=
92°
,
P
=
133°
(v)
M
=
59°
,
N
=
73°
,
O
=
91°
,
P
=
137°
Question
13
13.
Two adjacent angles of a parallelogram OPQR are in the ratio 10 : 26. Find the measure of each of its angles.
(i)
O
=
52°
,
P
=
129°
,
Q
=
48°
,
R
=
131°
(ii)
O
=
48°
,
P
=
132°
,
Q
=
49°
,
R
=
131°
(iii)
O
=
50°
,
P
=
130°
,
Q
=
50°
,
R
=
130°
(iv)
O
=
49°
,
P
=
128°
,
Q
=
51°
,
R
=
132°
(v)
O
=
51°
,
P
=
129°
,
Q
=
52°
,
R
=
128°
Question
14
14.
In the adjoining figure,
GHIJ
is a parallelogram in which
∠JGI = 16.49°
,
∠IGH = 14.76°
,
∠JKI = 101.89°
. Calculate
∠GHJ
(i)
64.35°
(ii)
63.35°
(iii)
65.35°
(iv)
62.35°
(v)
61.35°
Question
15
15.
In the adjoining figure,
OPQR
is a parallelogram in which
∠ROQ = 17.28°
,
∠QOP = 21.1°
,
∠RSQ = 70.95°
. Calculate
∠QRP
(i)
87.95°
(ii)
89.95°
(iii)
86.95°
(iv)
85.95°
(v)
88.95°
Question
16
16.
In the adjoining figure,
NOPQ
is a parallelogram in which
∠QNP = 31.83°
,
∠PNO = 37.57°
,
∠QRP = 80.5°
. Calculate
∠OPN
(i)
32.83°
(ii)
29.83°
(iii)
31.83°
(iv)
30.83°
(v)
33.83°
Question
17
17.
In the adjoining figure,
KLMN
is a parallelogram in which
∠NKM = 19.56°
,
∠MKL = 17.31°
,
∠NOM = 101.13°
. Calculate
∠NLM
(i)
82.57°
(ii)
80.57°
(iii)
79.57°
(iv)
81.57°
(v)
83.57°
Question
18
18.
In the adjoining figure,
CDEF
is a rectangle.
If
∠ECD = 46.85°
, find
∠DEC
(i)
45.15°
(ii)
41.15°
(iii)
44.15°
(iv)
43.15°
(v)
42.15°
Question
19
19.
Three angles of quadrilateral measure 85.62°, 94.78° and 53.13° respectively. Find the measure of the fourth angle
(i)
126.47°
(ii)
124.47°
(iii)
128.47°
(iv)
127.47°
(v)
125.47°
Question
20
20.
Three angles of a quadrilateral are equal and the fourth angle measure 47.91°. What is the measure of each of the equal angles?
(i)
105.03°
(ii)
103.03°
(iii)
104.03°
(iv)
102.03°
(v)
106.03°
Question
21
21.
Two angles of a quadrilateral are of measure 53.78° and 111.99° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
96.12°
(ii)
97.12°
(iii)
99.12°
(iv)
98.12°
(v)
95.12°
Question
22
22.
A quadrilateral has three acute angles, each measuring 60°. What is the measure of its fourth angle?
(i)
180.00°
(ii)
178.00°
(iii)
181.00°
(iv)
179.00°
(v)
182.00°
Question
23
23.
One angle of a parallelogram measures
J
=
69.51°
.
Find the measure of each of its remaining angles.
(i)
K
=
108.49°
,
L
=
67.51°
,
M
=
108.49°
(ii)
K
=
110.49°
,
L
=
69.51°
,
M
=
110.49°
(iii)
K
=
111.49°
,
L
=
70.51°
,
M
=
111.49°
(iv)
K
=
112.49°
,
L
=
71.51°
,
M
=
112.49°
(v)
K
=
109.49°
,
L
=
68.51°
,
M
=
109.49°
Question
24
24.
Two adjacent angles of a parallelogram are in the ratio
3 : 3
.
Find the measure of each of its angles.
(i)
A
=
92°
,
B
=
89°
,
C
=
88°
,
D
=
91°
(ii)
A
=
88°
,
B
=
92°
,
C
=
89°
,
D
=
91°
(iii)
A
=
90°
,
B
=
90°
,
C
=
90°
,
D
=
90°
(iv)
A
=
89°
,
B
=
88°
,
C
=
91°
,
D
=
92°
(v)
A
=
91°
,
B
=
89°
,
C
=
92°
,
D
=
88°
Question
25
25.
In the figure given below,
LMNO
is a rectangle.
Find the values of x and y
(i)
x
=
37.39°
,
y
=
73.78°
(ii)
x
=
38.39°
,
y
=
74.78°
(iii)
x
=
36.39°
,
y
=
72.78°
(iv)
x
=
35.39°
,
y
=
71.78°
(v)
x
=
34.39°
,
y
=
70.78°
Question
26
26.
In the figure given below,
ABCD
is a rectangle.
Find the values of x and y
(i)
x
=
48.12°
,
y
=
43.88°
(ii)
x
=
47.12°
,
y
=
42.88°
(iii)
x
=
45.12°
,
y
=
40.88°
(iv)
x
=
49.12°
,
y
=
44.88°
(v)
x
=
46.12°
,
y
=
41.88°
Question
27
27.
In the figure given below,
BCDE
is a rhombus.
Find the values of x and y
(i)
x
=
42.76°
,
y
=
42.76°
(ii)
x
=
44.76°
,
y
=
44.76°
(iii)
x
=
43.76°
,
y
=
43.76°
(iv)
x
=
41.76°
,
y
=
41.76°
(v)
x
=
40.76°
,
y
=
40.76°
Question
28
28.
In the figure given below,
BCDE
is a rhombus.
Find the values of x and y
(i)
x
=
44.95°
,
y
=
44.95°
(ii)
x
=
41.95°
,
y
=
41.95°
(iii)
x
=
43.95°
,
y
=
43.95°
(iv)
x
=
40.95°
,
y
=
40.95°
(v)
x
=
42.95°
,
y
=
42.95°
Question
29
29.
In the figure given below,
PQRS
is a rhombus.
Find the values of x and y
(i)
x
=
37.05°
,
y
=
50.95°
(ii)
x
=
40.05°
,
y
=
53.95°
(iii)
x
=
39.05°
,
y
=
52.95°
(iv)
x
=
38.05°
,
y
=
51.95°
(v)
x
=
36.05°
,
y
=
49.95°
Question
30
30.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
A
=
60°
,
B
=
120°
,
C
=
60°
,
D
=
120°
(ii)
A
=
59°
,
B
=
118°
,
C
=
61°
,
D
=
122°
(iii)
A
=
61°
,
B
=
119°
,
C
=
62°
,
D
=
118°
(iv)
A
=
58°
,
B
=
122°
,
C
=
59°
,
D
=
121°
(v)
A
=
62°
,
B
=
119°
,
C
=
58°
,
D
=
121°
Question
31
31.
In the adjoining figure,
ABCD
is a trapezium in which
AB
∥
CD
.
If
x = 98.91°
and
y = 122.11°
,
find the measures of
∠A
and
∠B
.
(i)
A
=
55.89°
,
B
=
79.09°
(ii)
A
=
56.89°
,
B
=
80.09°
(iii)
A
=
57.89°
,
B
=
81.09°
(iv)
A
=
58.89°
,
B
=
82.09°
(v)
A
=
59.89°
,
B
=
83.09°
Question
32
32.
In the adjoining figure,
ABCD
is a kite in which
AB
=
DA
,
BC
=
CD
and the diagonals
BD
and
AC
intersect at
O
.
If ∠OCD = 34.63° and ∠ABO = 41.86°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 55.37° , b = 49.14° , c = 40.86° , d = 57.37° , e = 32.63°
(ii)
a = 55.37° , b = 49.14° , c = 41.86° , d = 55.37° , e = 34.63°
(iii)
a = 55.37° , b = 49.14° , c = 40.86° , d = 57.37° , e = 34.63°
(iv)
a = 55.37° , b = 48.14° , c = 41.86° , d = 55.37° , e = 34.63°
(v)
a = 55.37° , b = 49.14° , c = 40.86° , d = 55.37° , e = 34.63°
Question
33
33.
In the adjoining figure, side EF of parallelogram DEFG has been produced to H. If ∠DEH = 35.19° , find the measure of each angle of the parallelogram.
(i)
D
=
36.19°
,
E
=
143.81°
,
F
=
37.19°
,
G
=
142.81°
(ii)
D
=
37.19°
,
E
=
143.81°
,
F
=
33.19°
,
G
=
145.81°
(iii)
D
=
33.19°
,
E
=
146.81°
,
F
=
34.19°
,
G
=
145.81°
(iv)
D
=
34.19°
,
E
=
142.81°
,
F
=
36.19°
,
G
=
146.81°
(v)
D
=
35.19°
,
E
=
144.81°
,
F
=
35.19°
,
G
=
144.81°
Question
34
34.
In the adjoining figure,
FGHI
is a parallelogram and
JK
is such that
JK
∥
FH
If
∠FIJ = 32.91°
and
∠HIK = 39.56°
,
find the measure of
∠FGH
.
(i)
108.53°
(ii)
105.53°
(iii)
107.53°
(iv)
106.53°
(v)
109.53°
Question
35
35.
In the adjoining figure, LMNO is a square. A line segment OQ cuts the side MN at Q and the diagonal LN at P such that ∠OPN = 100.31° and ∠PQN = x°. Find the value of x .
(i)
53.31°
(ii)
55.31°
(iii)
57.31°
(iv)
54.31°
(v)
56.31°
Question
36
36.
In the adjoining figure, CDEF is a rhombus and △GFE is an equilateral triangle. G and C are on opposite sides of EF. If ∠CDE = 36.07°, find the values of x and y .
(i)
x
=
39.97°
,
y
=
28°
(ii)
x
=
42.97°
,
y
=
31°
(iii)
x
=
43.97°
,
y
=
32°
(iv)
x
=
40.97°
,
y
=
29°
(v)
x
=
41.97°
,
y
=
30°
Question
37
37.
In the adjoining figure, equilateral △LKM surmounts square IJKL. If KMJ = x°, find the value of x.
(i)
15°
(ii)
16°
(iii)
14°
(iv)
17°
(v)
13°
Question
38
38.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
3 : 3
,
find the angles of
△OAB
.
(i)
O
=
92°
,
A
=
45°
,
B
=
43°
(ii)
O
=
88°
,
A
=
45°
,
B
=
47°
(iii)
O
=
90°
,
A
=
43°
,
B
=
47°
(iv)
O
=
90°
,
A
=
45°
,
B
=
45°
(v)
O
=
88°
,
A
=
47°
,
B
=
45°
Question
39
39.
In the given figure,
NOPQ
is a rectangle whose diagonals intersect at
R
.
Diagonal
OQ
is produced to
T
and
∠POT =
125.84°
. Find the angles of
△RPQ
.
(i)
R
=
108.32°
,
P
=
35.84°
,
Q
=
35.84°
(ii)
R
=
106.32°
,
P
=
35.84°
,
Q
=
37.84°
(iii)
R
=
108.32°
,
P
=
33.84°
,
Q
=
37.84°
(iv)
R
=
110.32°
,
P
=
35.84°
,
Q
=
33.84°
(v)
R
=
106.32°
,
P
=
37.84°
,
Q
=
35.84°
Question
40
40.
In the given figure,
IJKL
is a kite whose diagonals intersect at
M
.
If
∠LIJ = 94.77°
and
∠IJK = 76.44°
, calculate
∠MLI
and
∠MKL
.
(i)
x
=
43.62°
,
y
=
57.18°
(ii)
x
=
40.62°
,
y
=
54.18°
(iii)
x
=
42.62°
,
y
=
56.18°
(iv)
x
=
41.62°
,
y
=
55.18°
(v)
x
=
44.62°
,
y
=
58.18°
Question
41
41.
△HGD
is an equilateral triangle in a square
DEFG
.
If
DF
and
HG
intersect at
I
,
then find the value of x.
(i)
75°
(ii)
74°
(iii)
77°
(iv)
73°
(v)
76°
Question
42
42.
In the adjoining figure,
J
is a point in the interior of
∠LHM
.
If
JI
⟂
HL
and
JK
⟂
HM
and
∠LHM = 39°
,
find the measure of x .
(i)
139°
(ii)
142°
(iii)
140°
(iv)
141°
(v)
143°
Question
43
43.
In the given figure, DEFG is a parallelogram.
If
DU
and
EU
are bisector of
∠D
&
∠E
, find
∠U
(i)
92°
(ii)
88°
(iii)
90°
(iv)
91°
(v)
89°
Question
44
44.
In the given figure, DEFG is a parallelogram. U is the mid-point of FG.
EU
bisects
∠E
. If x =
52°
, find angle 'y'.
(i)
36°
(ii)
39°
(iii)
38°
(iv)
40°
(v)
37°
Question
45
45.
In the given figure, HIJK is a quadrilateral. RK and RJ are bisectors of ∠K & ∠J meeting at R. Find ∠JRK
(i)
85.5°
(ii)
87.5°
(iii)
83.5°
(iv)
86.5°
(v)
84.5°
Question
46
46.
In the given figure, EFGH is a rhombus. Given x = 58°, find the value of 'y'.
(i)
34°
(ii)
31°
(iii)
32°
(iv)
30°
(v)
33°
Question
47
47.
In the given figure, FGHI is a parallelogram. GI is the diagonal
such that
FI = GI = GH
. Given
∠F = 50°
, find
∠IGH
(i)
80°
(ii)
79°
(iii)
78°
(iv)
82°
(v)
81°
Question
48
48.
In the given figure, CDEF is a parallelogram. CP and EQ are perpendicular to the diagonal DF. Given ∠QEF = 44°, find ∠FDC
(i)
47°
(ii)
44°
(iii)
46°
(iv)
48°
(v)
45°
Question
49
49.
In the given figure, FGHI is a rhombus such that ∠G = 120°. Then △FGI is
(i)
Obtuse angled triangle
(ii)
Equilateral triangle
(iii)
Isosceles triangle
(iv)
Right angled triangle
Question
50
50.
BCDE is a rhombus. O, P, Q and R are mid-points of sides BC, CD, DE and EB. Find ∠PQR
(i)
89°
(ii)
90°
(iii)
88°
(iv)
92°
(v)
91°
Question
51
51.
In the given figure, BCDE is a parallelogram such that S is the mid-point of BC and BC = 2EB. Find ∠ESD
(i)
91°
(ii)
90°
(iii)
89°
(iv)
88°
(v)
92°
Question
52
52.
FGHI is an isosceles trapezium. FR and GR are angular bisector of ∠F & ∠G. If ∠F = 57°, find ∠FRG
(i)
123°
(ii)
125°
(iii)
124°
(iv)
122°
(v)
121°
Question
53
53.
In the given figure, DEFG is a parallelogram. The bisector of the angles D, E, F & G intersect at Q, R, S & T to form a quadrilateral. Find ∠QRS
(i)
89°
(ii)
91°
(iii)
92°
(iv)
90°
(v)
88°
Assignment Key
1) (ii)
2) (i)
3) (iii)
4) (i)
5) (iii)
6) (i)
7) (iii)
8) (iv)
9) (iv)
10) (iii)
11) (iv)
12) (i)
13) (iii)
14) (ii)
15) (i)
16) (iii)
17) (iv)
18) (iv)
19) (i)
20) (iii)
21) (ii)
22) (i)
23) (ii)
24) (iii)
25) (iii)
26) (ii)
27) (i)
28) (v)
29) (iv)
30) (i)
31) (iii)
32) (iv)
33) (v)
34) (iii)
35) (ii)
36) (v)
37) (i)
38) (iv)
39) (i)
40) (iii)
41) (i)
42) (iv)
43) (iii)
44) (iii)
45) (i)
46) (iii)
47) (i)
48) (iii)
49) (ii)
50) (ii)
51) (ii)
52) (i)
53) (iv)
