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)
133.99°
(ii)
143.99°
(iii)
148.99°
(iv)
138.99°
(v)
163.99°
Question
2
2.
Find the missing angle in the given trapezium
(i)
131.72°
(ii)
101.72°
(iii)
111.72°
(iv)
116.72°
(v)
106.72°
Question
3
3.
Find the missing angle in the given parallelogram
(i)
53.13°
(ii)
83.13°
(iii)
58.13°
(iv)
63.13°
(v)
68.13°
Question
4
4.
Find the missing angle in the given rhombus
(i)
112.36°
(ii)
122.36°
(iii)
142.36°
(iv)
127.36°
(v)
117.36°
Question
5
5.
The measures of three angles of a quadrilateral are
52.62°
,
133.35°
and
65.37°
. Find the fourth angle
(i)
113.66°
(ii)
123.66°
(iii)
118.66°
(iv)
138.66°
(v)
108.66°
Question
6
6.
Sum of the interior angles in a quadrilateral is
(i)
370°
(ii)
390°
(iii)
360°
(iv)
375°
(v)
365°
Question
7
7.
In parallelogram ABCD, if ∠C = 29.76°, then find the value of ∠A
(i)
28.76°
(ii)
31.76°
(iii)
27.76°
(iv)
29.76°
(v)
30.76°
Question
8
8.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
89°
(ii)
88°
(iii)
91°
(iv)
92°
(v)
90°
Question
9
9.
If ABCD is an isosceles trapezium, ∠D =
(i)
∠A
(ii)
90°
(iii)
∠B
(iv)
∠C
Question
10
10.
GHIJ is a rhombus in which ∠G = 120° .
HJ
is the diagonal. Then △GHI is
(i)
an obtuse angled triangle
(ii)
an isosceles triangle
(iii)
None of these
(iv)
an equilateral triangle
(v)
a scalene triangle
Question
11
11.
ABCD is a rhombus in which ∠A = 81° .
BD
is the diagonal. Then △ABC is
(i)
an isosceles triangle
(ii)
a scalene triangle
(iii)
an equilateral triangle
(iv)
an obtuse angled triangle
(v)
None of these
Question
12
12.
The angles of a quadrilateral NOPQ are in the ratio 16 : 8 : 9 : 39. Find the measure of each angle of the quadrilateral.
(i)
N
=
78°
,
O
=
42°
,
P
=
44°
,
Q
=
196°
(ii)
N
=
80°
,
O
=
40°
,
P
=
45°
,
Q
=
195°
(iii)
N
=
82°
,
O
=
39°
,
P
=
43°
,
Q
=
196°
(iv)
N
=
79°
,
O
=
38°
,
P
=
46°
,
Q
=
197°
(v)
N
=
81°
,
O
=
39°
,
P
=
47°
,
Q
=
193°
Question
13
13.
Two adjacent angles of a parallelogram FGHI are in the ratio 2 : 18. Find the measure of each of its angles.
(i)
F
=
18°
,
G
=
162°
,
H
=
18°
,
I
=
162°
(ii)
F
=
17°
,
G
=
160°
,
H
=
19°
,
I
=
164°
(iii)
F
=
19°
,
G
=
161°
,
H
=
20°
,
I
=
160°
(iv)
F
=
20°
,
G
=
161°
,
H
=
16°
,
I
=
163°
(v)
F
=
16°
,
G
=
164°
,
H
=
17°
,
I
=
163°
Question
14
14.
In the adjoining figure,
DEFG
is a parallelogram in which
∠GDF = 31.66°
,
∠FDE = 49.7°
,
∠GHF = 68.86°
. Calculate
∠DEG
(i)
59.44°
(ii)
62.44°
(iii)
61.44°
(iv)
60.44°
(v)
63.44°
Question
15
15.
In the adjoining figure,
ABCD
is a parallelogram in which
∠DAC = 43.17°
,
∠CAB = 23.86°
,
∠DEC = 121.05°
. Calculate
∠CDB
(i)
36.09°
(ii)
34.09°
(iii)
37.09°
(iv)
33.09°
(v)
35.09°
Question
16
16.
In the adjoining figure,
MNOP
is a parallelogram in which
∠PMO = 33.85°
,
∠OMN = 23.41°
,
∠PQO = 112.27°
. Calculate
∠NOM
(i)
32.85°
(ii)
33.85°
(iii)
34.85°
(iv)
31.85°
(v)
35.85°
Question
17
17.
In the adjoining figure,
IJKL
is a parallelogram in which
∠LIK = 30.29°
,
∠KIJ = 22°
,
∠LMK = 109.65°
. Calculate
∠LJK
(i)
79.36°
(ii)
80.36°
(iii)
77.36°
(iv)
78.36°
(v)
81.36°
Question
18
18.
In the adjoining figure,
CDEF
is a rectangle.
If
∠ECD = 46.55°
, find
∠DEC
(i)
43.45°
(ii)
42.45°
(iii)
44.45°
(iv)
41.45°
(v)
45.45°
Question
19
19.
Three angles of quadrilateral measure 119.22°, 31.79° and 81.79° respectively. Find the measure of the fourth angle
(i)
129.20°
(ii)
125.20°
(iii)
127.20°
(iv)
126.20°
(v)
128.20°
Question
20
20.
Three angles of a quadrilateral are equal and the fourth angle measure 138.94°. What is the measure of each of the equal angles?
(i)
74.69°
(ii)
72.69°
(iii)
73.69°
(iv)
75.69°
(v)
71.69°
Question
21
21.
Two angles of a quadrilateral are of measure 98.22° and 115.25° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
73.27°
(ii)
72.27°
(iii)
74.27°
(iv)
75.27°
(v)
71.27°
Question
22
22.
A quadrilateral has three acute angles, each measuring 61°. What is the measure of its fourth angle?
(i)
179.00°
(ii)
177.00°
(iii)
178.00°
(iv)
175.00°
(v)
176.00°
Question
23
23.
One angle of a parallelogram measures
E
=
56.25°
.
Find the measure of each of its remaining angles.
(i)
F
=
122.75°
,
G
=
55.25°
,
H
=
122.75°
(ii)
F
=
125.75°
,
G
=
58.25°
,
H
=
125.75°
(iii)
F
=
121.75°
,
G
=
54.25°
,
H
=
121.75°
(iv)
F
=
123.75°
,
G
=
56.25°
,
H
=
123.75°
(v)
F
=
124.75°
,
G
=
57.25°
,
H
=
124.75°
Question
24
24.
Two adjacent angles of a parallelogram are in the ratio
7 : 11
.
Find the measure of each of its angles.
(i)
A
=
72°
,
B
=
109°
,
C
=
68°
,
D
=
111°
(ii)
A
=
71°
,
B
=
109°
,
C
=
72°
,
D
=
108°
(iii)
A
=
70°
,
B
=
110°
,
C
=
70°
,
D
=
110°
(iv)
A
=
69°
,
B
=
108°
,
C
=
71°
,
D
=
112°
(v)
A
=
68°
,
B
=
112°
,
C
=
69°
,
D
=
111°
Question
25
25.
In the figure given below,
JKLM
is a rectangle.
Find the values of x and y
(i)
x
=
52.78°
,
y
=
107.56°
(ii)
x
=
56.78°
,
y
=
111.56°
(iii)
x
=
54.78°
,
y
=
109.56°
(iv)
x
=
55.78°
,
y
=
110.56°
(v)
x
=
53.78°
,
y
=
108.56°
Question
26
26.
In the figure given below,
IJKL
is a rectangle.
Find the values of x and y
(i)
x
=
50.34°
,
y
=
37.66°
(ii)
x
=
49.34°
,
y
=
36.66°
(iii)
x
=
52.34°
,
y
=
39.66°
(iv)
x
=
53.34°
,
y
=
40.66°
(v)
x
=
51.34°
,
y
=
38.66°
Question
27
27.
In the figure given below,
GHIJ
is a rhombus.
Find the values of x and y
(i)
x
=
33.15°
,
y
=
33.15°
(ii)
x
=
34.15°
,
y
=
34.15°
(iii)
x
=
31.15°
,
y
=
31.15°
(iv)
x
=
30.15°
,
y
=
30.15°
(v)
x
=
32.15°
,
y
=
32.15°
Question
28
28.
In the figure given below,
KLMN
is a rhombus.
Find the values of x and y
(i)
x
=
73.08°
,
y
=
73.08°
(ii)
x
=
75.08°
,
y
=
75.08°
(iii)
x
=
74.08°
,
y
=
74.08°
(iv)
x
=
76.08°
,
y
=
76.08°
(v)
x
=
72.08°
,
y
=
72.08°
Question
29
29.
In the figure given below,
KLMN
is a rhombus.
Find the values of x and y
(i)
x
=
31.21°
,
y
=
56.79°
(ii)
x
=
30.21°
,
y
=
55.79°
(iii)
x
=
32.21°
,
y
=
57.79°
(iv)
x
=
33.21°
,
y
=
58.79°
(v)
x
=
34.21°
,
y
=
59.79°
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
=
61°
,
B
=
119°
,
C
=
62°
,
D
=
118°
(ii)
A
=
62°
,
B
=
119°
,
C
=
58°
,
D
=
121°
(iii)
A
=
58°
,
B
=
122°
,
C
=
59°
,
D
=
121°
(iv)
A
=
59°
,
B
=
118°
,
C
=
61°
,
D
=
122°
(v)
A
=
60°
,
B
=
120°
,
C
=
60°
,
D
=
120°
Question
31
31.
In the adjoining figure,
BCDE
is a trapezium in which
BC
∥
DE
.
If
x = 96.97°
and
y = 131.28°
,
find the measures of
∠B
and
∠C
.
(i)
B
=
47.72°
,
C
=
82.03°
(ii)
B
=
48.72°
,
C
=
83.03°
(iii)
B
=
50.72°
,
C
=
85.03°
(iv)
B
=
46.72°
,
C
=
81.03°
(v)
B
=
49.72°
,
C
=
84.03°
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 = 31.84° and ∠ABO = 51.63°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 58.16° , b = 39.37° , c = 50.63° , d = 60.16° , e = 29.84°
(ii)
a = 58.16° , b = 39.37° , c = 50.63° , d = 60.16° , e = 31.84°
(iii)
a = 58.16° , b = 39.37° , c = 50.63° , d = 58.16° , e = 31.84°
(iv)
a = 58.16° , b = 38.37° , c = 51.63° , d = 58.16° , e = 31.84°
(v)
a = 58.16° , b = 39.37° , c = 51.63° , d = 58.16° , e = 31.84°
Question
33
33.
In the adjoining figure, side LM of parallelogram KLMN has been produced to O. If ∠KLO = 48.82° , find the measure of each angle of the parallelogram.
(i)
K
=
50.82°
,
L
=
130.18°
,
M
=
46.82°
,
N
=
132.18°
(ii)
K
=
47.82°
,
L
=
129.18°
,
M
=
49.82°
,
N
=
133.18°
(iii)
K
=
46.82°
,
L
=
133.18°
,
M
=
47.82°
,
N
=
132.18°
(iv)
K
=
48.82°
,
L
=
131.18°
,
M
=
48.82°
,
N
=
131.18°
(v)
K
=
49.82°
,
L
=
130.18°
,
M
=
50.82°
,
N
=
129.18°
Question
34
34.
In the adjoining figure,
NOPQ
is a parallelogram and
RS
is such that
RS
∥
NP
If
∠NQR = 25.71°
and
∠PQS = 24.58°
,
find the measure of
∠PQN
.
(i)
129.71°
(ii)
130.71°
(iii)
128.71°
(iv)
127.71°
(v)
131.71°
Question
35
35.
In the adjoining figure, BCDE is a square. A line segment EG cuts the side CD at G and the diagonal BD at F such that ∠EFD = 90.68° and ∠FGD = x°. Find the value of x .
(i)
46.68°
(ii)
45.68°
(iii)
47.68°
(iv)
44.68°
(v)
43.68°
Question
36
36.
In the adjoining figure, EFGH is a rhombus and △IHG is an equilateral triangle. I and F are on opposite sides of GH. If ∠HEF = 81.19°, find the values of x and y .
(i)
x
=
28°
,
y
=
17.41°
(ii)
x
=
32°
,
y
=
21.41°
(iii)
x
=
29°
,
y
=
18.41°
(iv)
x
=
31°
,
y
=
20.41°
(v)
x
=
30°
,
y
=
19.41°
Question
37
37.
In the adjoining figure, equilateral △IHJ surmounts square FGHI. If HJG = x°, find the value of x.
(i)
14°
(ii)
17°
(iii)
15°
(iv)
16°
(v)
13°
Question
38
38.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
2 : 13
,
find the angles of
△OAB
.
(i)
O
=
92°
,
A
=
12°
,
B
=
76°
(ii)
O
=
88°
,
A
=
12°
,
B
=
80°
(iii)
O
=
90°
,
A
=
12°
,
B
=
78°
(iv)
O
=
88°
,
A
=
14°
,
B
=
78°
(v)
O
=
90°
,
A
=
10°
,
B
=
80°
Question
39
39.
In the given figure,
EFGH
is a rectangle whose diagonals intersect at
I
.
Diagonal
EG
is produced to
T
and
∠FET =
128.16°
. Find the angles of
△IGH
.
(i)
I
=
76.32°
,
G
=
51.84°
,
H
=
51.84°
(ii)
I
=
78.32°
,
G
=
51.84°
,
H
=
49.84°
(iii)
I
=
74.32°
,
G
=
51.84°
,
H
=
53.84°
(iv)
I
=
76.32°
,
G
=
49.84°
,
H
=
53.84°
(v)
I
=
74.32°
,
G
=
53.84°
,
H
=
51.84°
Question
40
40.
In the given figure,
EFGH
is a kite whose diagonals intersect at
I
.
If
∠HEF = 46.64°
and
∠FGH = 32.24°
, calculate
∠IHE
and
∠IFG
.
(i)
x
=
66.68°
,
y
=
73.88°
(ii)
x
=
67.68°
,
y
=
74.88°
(iii)
x
=
64.68°
,
y
=
71.88°
(iv)
x
=
68.68°
,
y
=
75.88°
(v)
x
=
65.68°
,
y
=
72.88°
Question
41
41.
△OLM
is an equilateral triangle in a square
KLMN
.
If
LN
and
MO
intersect at
P
,
then find the value of x.
(i)
76°
(ii)
74°
(iii)
75°
(iv)
73°
(v)
77°
Question
42
42.
In the adjoining figure,
C
is a point in the interior of
∠EAF
.
If
CB
⟂
AE
and
CD
⟂
AF
and
∠EAF = 30°
,
find the measure of x .
(i)
212°
(ii)
210°
(iii)
209°
(iv)
208°
(v)
211°
Question
43
43.
In the given figure, EFGH is a parallelogram.
If
ER
and
FR
are bisector of
∠E
&
∠F
, find
∠R
(i)
88°
(ii)
92°
(iii)
90°
(iv)
91°
(v)
89°
Question
44
44.
In the given figure, CDEF is a parallelogram. P is the mid-point of EF.
DP
bisects
∠D
. If x =
52°
, find angle 'y'.
(i)
37°
(ii)
40°
(iii)
36°
(iv)
38°
(v)
39°
Question
45
45.
In the given figure, DEFG is a quadrilateral. QG and QF are bisectors of ∠G & ∠F meeting at Q. Find ∠FQG
(i)
94.5°
(ii)
92.5°
(iii)
96.5°
(iv)
93.5°
(v)
95.5°
Question
46
46.
In the given figure, BCDE is a rhombus. Given x = 56°, find the value of 'y'.
(i)
34°
(ii)
32°
(iii)
35°
(iv)
36°
(v)
33°
Question
47
47.
In the given figure, IJKL is a parallelogram. JL is the diagonal
such that
IL = JL = JK
. Given
∠I = 55°
, find
∠LJK
(i)
70°
(ii)
71°
(iii)
72°
(iv)
68°
(v)
69°
Question
48
48.
In the given figure, CDEF is a parallelogram. CQ and ER are perpendicular to the diagonal DF. Given ∠REF = 30°, find ∠FDC
(i)
60°
(ii)
59°
(iii)
62°
(iv)
58°
(v)
61°
Question
49
49.
In the given figure, HIJK is a rhombus such that ∠I = 120°. Then △HIK is
(i)
Isosceles triangle
(ii)
Equilateral triangle
(iii)
Obtuse angled triangle
(iv)
Right angled triangle
Question
50
50.
CDEF is a rhombus. M, N, O and P are mid-points of sides CD, DE, EF and FC. Find ∠NOP
(i)
92°
(ii)
89°
(iii)
90°
(iv)
91°
(v)
88°
Question
51
51.
In the given figure, CDEF is a parallelogram such that R is the mid-point of CD and CD = 2FC. Find ∠FRE
(i)
90°
(ii)
92°
(iii)
88°
(iv)
91°
(v)
89°
Question
52
52.
GHIJ is an isosceles trapezium. GQ and HQ are angular bisector of ∠G & ∠H. If ∠G = 64°, find ∠GQH
(i)
115°
(ii)
118°
(iii)
114°
(iv)
116°
(v)
117°
Question
53
53.
In the given figure, DEFG is a parallelogram. The bisector of the angles D, E, F & G intersect at R, S, T & U to form a quadrilateral. Find ∠TUR
(i)
88°
(ii)
90°
(iii)
92°
(iv)
89°
(v)
91°
Assignment Key
1) (i)
2) (ii)
3) (i)
4) (i)
5) (v)
6) (iii)
7) (iv)
8) (v)
9) (iv)
10) (iv)
11) (i)
12) (ii)
13) (i)
14) (iii)
15) (v)
16) (ii)
17) (i)
18) (i)
19) (iii)
20) (iii)
21) (i)
22) (ii)
23) (iv)
24) (iii)
25) (iii)
26) (v)
27) (v)
28) (iii)
29) (iii)
30) (v)
31) (ii)
32) (iv)
33) (iv)
34) (i)
35) (ii)
36) (v)
37) (iii)
38) (iii)
39) (i)
40) (i)
41) (iii)
42) (ii)
43) (iii)
44) (iv)
45) (i)
46) (i)
47) (i)
48) (i)
49) (ii)
50) (iii)
51) (i)
52) (iv)
53) (ii)
