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)
133.58°
(ii)
118.58°
(iii)
103.58°
(iv)
108.58°
(v)
113.58°
Question
2
2.
Find the missing angle in the given trapezium
(i)
100.97°
(ii)
125.97°
(iii)
95.97°
(iv)
110.97°
(v)
105.97°
Question
3
3.
Find the missing angle in the given parallelogram
(i)
139.04°
(ii)
129.04°
(iii)
134.04°
(iv)
159.04°
(v)
144.04°
Question
4
4.
Find the missing angle in the given rhombus
(i)
73.4°
(ii)
78.4°
(iii)
68.4°
(iv)
98.4°
(v)
83.4°
Question
5
5.
The measures of three angles of a quadrilateral are
54.56°
,
125.68°
and
62.97°
. Find the fourth angle
(i)
126.79°
(ii)
116.79°
(iii)
131.79°
(iv)
121.79°
(v)
146.79°
Question
6
6.
Sum of the interior angles in a quadrilateral is
(i)
365°
(ii)
375°
(iii)
360°
(iv)
390°
(v)
370°
Question
7
7.
In parallelogram ABCD, if ∠D = 159.64°, then find the value of ∠A
(i)
18.36°
(ii)
21.36°
(iii)
19.36°
(iv)
22.36°
(v)
20.36°
Question
8
8.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
88°
(ii)
89°
(iii)
92°
(iv)
90°
(v)
91°
Question
9
9.
If ABCD is an isosceles trapezium, ∠B =
(i)
∠C
(ii)
∠D
(iii)
90°
(iv)
∠A
Question
10
10.
JKLM is a rhombus in which ∠J = 120° .
KM
is the diagonal. Then △JKL is
(i)
an equilateral triangle
(ii)
None of these
(iii)
a scalene triangle
(iv)
an isosceles triangle
(v)
an obtuse angled triangle
Question
11
11.
LMNO is a rhombus in which ∠L = 117° .
MO
is the diagonal. Then △LMN is
(i)
None of these
(ii)
an obtuse angled triangle
(iii)
an equilateral triangle
(iv)
an isosceles triangle
(v)
a scalene triangle
Question
12
12.
The angles of a quadrilateral KLMN are in the ratio 25 : 23 : 15 : 57. Find the measure of each angle of the quadrilateral.
(i)
K
=
77°
,
L
=
68°
,
M
=
43°
,
N
=
172°
(ii)
K
=
73°
,
L
=
71°
,
M
=
44°
,
N
=
172°
(iii)
K
=
76°
,
L
=
68°
,
M
=
47°
,
N
=
169°
(iv)
K
=
74°
,
L
=
67°
,
M
=
46°
,
N
=
173°
(v)
K
=
75°
,
L
=
69°
,
M
=
45°
,
N
=
171°
Question
13
13.
Two adjacent angles of a parallelogram FGHI are in the ratio 17 : 19. Find the measure of each of its angles.
(i)
F
=
86°
,
G
=
94°
,
H
=
87°
,
I
=
93°
(ii)
F
=
84°
,
G
=
93°
,
H
=
86°
,
I
=
97°
(iii)
F
=
83°
,
G
=
97°
,
H
=
84°
,
I
=
96°
(iv)
F
=
85°
,
G
=
95°
,
H
=
85°
,
I
=
95°
(v)
F
=
87°
,
G
=
94°
,
H
=
83°
,
I
=
96°
Question
14
14.
In the adjoining figure,
MNOP
is a parallelogram in which
∠PMO = 13.51°
,
∠OMN = 26.38°
,
∠PQO = 42.96°
. Calculate
∠MNP
(i)
110.66°
(ii)
111.66°
(iii)
108.66°
(iv)
112.66°
(v)
109.66°
Question
15
15.
In the adjoining figure,
FGHI
is a parallelogram in which
∠IFH = 20.32°
,
∠HFG = 12.45°
,
∠IJH = 130.4°
. Calculate
∠HIG
(i)
35.15°
(ii)
37.15°
(iii)
38.15°
(iv)
39.15°
(v)
36.15°
Question
16
16.
In the adjoining figure,
IJKL
is a parallelogram in which
∠LIK = 22.55°
,
∠KIJ = 25.58°
,
∠LMK = 79.86°
. Calculate
∠JKI
(i)
24.55°
(ii)
23.55°
(iii)
21.55°
(iv)
22.55°
(v)
20.55°
Question
17
17.
In the adjoining figure,
LMNO
is a parallelogram in which
∠OLN = 34.24°
,
∠NLM = 20.15°
,
∠OPN = 120.59°
. Calculate
∠OMN
(i)
85.34°
(ii)
86.34°
(iii)
84.34°
(iv)
87.34°
(v)
88.34°
Question
18
18.
In the adjoining figure,
OPQR
is a rectangle.
If
∠QOP = 53.13°
, find
∠QSP
(i)
104.26°
(ii)
106.26°
(iii)
108.26°
(iv)
105.26°
(v)
107.26°
Question
19
19.
Three angles of quadrilateral measure 60°, 73.41° and 135.91° respectively. Find the measure of the fourth angle
(i)
89.68°
(ii)
92.68°
(iii)
90.68°
(iv)
91.68°
(v)
88.68°
Question
20
20.
Three angles of a quadrilateral are equal and the fourth angle measure 116.1°. What is the measure of each of the equal angles?
(i)
82.30°
(ii)
83.30°
(iii)
81.30°
(iv)
80.30°
(v)
79.30°
Question
21
21.
Two angles of a quadrilateral are of measure 135.91° and 77.73° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
75.18°
(ii)
74.18°
(iii)
71.18°
(iv)
72.18°
(v)
73.18°
Question
22
22.
A quadrilateral has three acute angles, each measuring 62°. What is the measure of its fourth angle?
(i)
176.00°
(ii)
174.00°
(iii)
173.00°
(iv)
172.00°
(v)
175.00°
Question
23
23.
One angle of a parallelogram measures
G
=
57.56°
.
Find the measure of each of its remaining angles.
(i)
H
=
120.44°
,
I
=
55.56°
,
J
=
120.44°
(ii)
H
=
123.44°
,
I
=
58.56°
,
J
=
123.44°
(iii)
H
=
122.44°
,
I
=
57.56°
,
J
=
122.44°
(iv)
H
=
124.44°
,
I
=
59.56°
,
J
=
124.44°
(v)
H
=
121.44°
,
I
=
56.56°
,
J
=
121.44°
Question
24
24.
Two adjacent angles of a parallelogram are in the ratio
21 : 39
.
Find the measure of each of its angles.
(i)
A
=
62°
,
B
=
115°
,
C
=
64°
,
D
=
119°
(ii)
A
=
65°
,
B
=
116°
,
C
=
61°
,
D
=
118°
(iii)
A
=
64°
,
B
=
116°
,
C
=
65°
,
D
=
115°
(iv)
A
=
61°
,
B
=
119°
,
C
=
62°
,
D
=
118°
(v)
A
=
63°
,
B
=
117°
,
C
=
63°
,
D
=
117°
Question
25
25.
In the figure given below,
LMNO
is a rectangle.
Find the values of x and y
(i)
x
=
35.99°
,
y
=
70.98°
(ii)
x
=
33.99°
,
y
=
68.98°
(iii)
x
=
36.99°
,
y
=
71.98°
(iv)
x
=
32.99°
,
y
=
67.98°
(v)
x
=
34.99°
,
y
=
69.98°
Question
26
26.
In the figure given below,
EFGH
is a rectangle.
Find the values of x and y
(i)
x
=
39.57°
,
y
=
54.43°
(ii)
x
=
38.57°
,
y
=
53.43°
(iii)
x
=
37.57°
,
y
=
52.43°
(iv)
x
=
35.57°
,
y
=
50.43°
(v)
x
=
36.57°
,
y
=
51.43°
Question
27
27.
In the figure given below,
DEFG
is a rhombus.
Find the values of x and y
(i)
x
=
30.4°
,
y
=
30.4°
(ii)
x
=
28.4°
,
y
=
28.4°
(iii)
x
=
27.4°
,
y
=
27.4°
(iv)
x
=
29.4°
,
y
=
29.4°
(v)
x
=
26.4°
,
y
=
26.4°
Question
28
28.
In the figure given below,
PQRS
is a rhombus.
Find the values of x and y
(i)
x
=
63.96°
,
y
=
63.96°
(ii)
x
=
61.96°
,
y
=
61.96°
(iii)
x
=
62.96°
,
y
=
62.96°
(iv)
x
=
64.96°
,
y
=
64.96°
(v)
x
=
60.96°
,
y
=
60.96°
Question
29
29.
In the figure given below,
KLMN
is a rhombus.
Find the values of x and y
(i)
x
=
42.82°
,
y
=
49.18°
(ii)
x
=
39.82°
,
y
=
46.18°
(iii)
x
=
41.82°
,
y
=
48.18°
(iv)
x
=
43.82°
,
y
=
50.18°
(v)
x
=
40.82°
,
y
=
47.18°
Question
30
30.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
D
=
59°
,
E
=
118°
,
F
=
61°
,
G
=
122°
(ii)
D
=
61°
,
E
=
119°
,
F
=
62°
,
G
=
118°
(iii)
D
=
58°
,
E
=
122°
,
F
=
59°
,
G
=
121°
(iv)
D
=
60°
,
E
=
120°
,
F
=
60°
,
G
=
120°
(v)
D
=
62°
,
E
=
119°
,
F
=
58°
,
G
=
121°
Question
31
31.
In the adjoining figure,
BCDE
is a trapezium in which
BC
∥
DE
.
If
x = 95.92°
and
y = 116.05°
,
find the measures of
∠B
and
∠C
.
(i)
B
=
65.95°
,
C
=
86.08°
(ii)
B
=
63.95°
,
C
=
84.08°
(iii)
B
=
64.95°
,
C
=
85.08°
(iv)
B
=
62.95°
,
C
=
83.08°
(v)
B
=
61.95°
,
C
=
82.08°
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 = 35.72° and ∠ABO = 63.43°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 54.28° , b = 27.57° , c = 62.43° , d = 56.28° , e = 33.72°
(ii)
a = 54.28° , b = 27.57° , c = 63.43° , d = 54.28° , e = 35.72°
(iii)
a = 54.28° , b = 26.57° , c = 63.43° , d = 54.28° , e = 35.72°
(iv)
a = 54.28° , b = 27.57° , c = 62.43° , d = 56.28° , e = 35.72°
(v)
a = 54.28° , b = 27.57° , c = 62.43° , d = 54.28° , e = 35.72°
Question
33
33.
In the adjoining figure, side JG of parallelogram GHIJ has been produced to K. If ∠HGK = 118.28° , find the measure of each angle of the parallelogram.
(i)
G
=
60.72°
,
H
=
116.28°
,
I
=
62.72°
,
J
=
120.28°
(ii)
G
=
63.72°
,
H
=
117.28°
,
I
=
59.72°
,
J
=
119.28°
(iii)
G
=
59.72°
,
H
=
120.28°
,
I
=
60.72°
,
J
=
119.28°
(iv)
G
=
62.72°
,
H
=
117.28°
,
I
=
63.72°
,
J
=
116.28°
(v)
G
=
61.72°
,
H
=
118.28°
,
I
=
61.72°
,
J
=
118.28°
Question
34
34.
In the adjoining figure,
GHIJ
is a parallelogram and
KL
is such that
KL
∥
GI
If
∠GJK = 15.83°
and
∠IJL = 21.04°
,
find the measure of
∠IJG
.
(i)
142.13°
(ii)
143.13°
(iii)
145.13°
(iv)
144.13°
(v)
141.13°
Question
35
35.
In the adjoining figure, PQRS is a square. A line segment SU cuts the side QR at U and the diagonal PR at T such that ∠STR = 111.14° and ∠TUR = x°. Find the value of x .
(i)
65.14°
(ii)
68.14°
(iii)
67.14°
(iv)
66.14°
(v)
64.14°
Question
36
36.
In the adjoining figure, KLMN is a rhombus and △ONM is an equilateral triangle. O and K are on opposite sides of MN. If ∠KLM = 49.4°, find the values of x and y .
(i)
x
=
33.3°
,
y
=
28°
(ii)
x
=
35.3°
,
y
=
30°
(iii)
x
=
34.3°
,
y
=
29°
(iv)
x
=
36.3°
,
y
=
31°
(v)
x
=
37.3°
,
y
=
32°
Question
37
37.
In the adjoining figure, equilateral △JIK surmounts square GHIJ. If IKG = x°, find the value of x.
(i)
45°
(ii)
46°
(iii)
43°
(iv)
47°
(v)
44°
Question
38
38.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
2 : 4
,
find the angles of
△OAB
.
(i)
O
=
90°
,
A
=
28°
,
B
=
62°
(ii)
O
=
88°
,
A
=
30°
,
B
=
62°
(iii)
O
=
90°
,
A
=
30°
,
B
=
60°
(iv)
O
=
88°
,
A
=
32°
,
B
=
60°
(v)
O
=
92°
,
A
=
30°
,
B
=
58°
Question
39
39.
In the given figure,
BCDE
is a rectangle whose diagonals intersect at
F
.
Diagonal
BD
is produced to
T
and
∠EDT =
140.91°
. Find the angles of
△FEB
.
(i)
F
=
78.18°
,
E
=
48.91°
,
B
=
52.91°
(ii)
F
=
78.18°
,
E
=
50.91°
,
B
=
50.91°
(iii)
F
=
76.18°
,
E
=
50.91°
,
B
=
52.91°
(iv)
F
=
76.18°
,
E
=
52.91°
,
B
=
50.91°
(v)
F
=
80.18°
,
E
=
50.91°
,
B
=
48.91°
Question
40
40.
In the given figure,
IJKL
is a kite whose diagonals intersect at
M
.
If
∠LIJ = 57.05°
and
∠JKL = 63.69°
, calculate
∠MLI
and
∠MJK
.
(i)
x
=
60.47°
,
y
=
57.16°
(ii)
x
=
59.47°
,
y
=
56.16°
(iii)
x
=
61.47°
,
y
=
58.16°
(iv)
x
=
62.47°
,
y
=
59.16°
(v)
x
=
63.47°
,
y
=
60.16°
Question
41
41.
△QOP
is an equilateral triangle in a square
MNOP
.
If
NP
and
QO
intersect at
R
,
then find the value of x.
(i)
73°
(ii)
75°
(iii)
77°
(iv)
74°
(v)
76°
Question
42
42.
In the adjoining figure,
D
is a point in the interior of
∠FBG
.
If
DC
⟂
BF
and
DE
⟂
BG
and
∠FBG = 57°
,
find the measure of x .
(i)
121°
(ii)
123°
(iii)
122°
(iv)
124°
(v)
125°
Question
43
43.
In the given figure, CDEF is a parallelogram.
If
CU
and
DU
are bisector of
∠C
&
∠D
, find
∠U
(i)
89°
(ii)
92°
(iii)
91°
(iv)
88°
(v)
90°
Question
44
44.
In the given figure, CDEF is a parallelogram. S is the mid-point of EF.
DS
bisects
∠D
. If x =
52°
, find angle 'y'.
(i)
37°
(ii)
38°
(iii)
36°
(iv)
39°
(v)
40°
Question
45
45.
In the given figure, DEFG is a quadrilateral. PG and PF are bisectors of ∠G & ∠F meeting at P. Find ∠FPG
(i)
84.0°
(ii)
86.0°
(iii)
87.0°
(iv)
88.0°
(v)
85.0°
Question
46
46.
In the given figure, EFGH is a rhombus. Given x = 58°, find the value of 'y'.
(i)
32°
(ii)
30°
(iii)
34°
(iv)
31°
(v)
33°
Question
47
47.
In the given figure, CDEF is a parallelogram. DF is the diagonal
such that
CF = DF = DE
. Given
∠C = 62°
, find
∠FDE
(i)
54°
(ii)
57°
(iii)
55°
(iv)
58°
(v)
56°
Question
48
48.
In the given figure, DEFG is a parallelogram. DM and FN are perpendicular to the diagonal EG. Given ∠MDE = 36°, find ∠FGE
(i)
52°
(ii)
53°
(iii)
55°
(iv)
56°
(v)
54°
Question
49
49.
In the given figure, BCDE is a rhombus such that ∠C = 120°. Then △BCE is
(i)
Isosceles triangle
(ii)
Right angled triangle
(iii)
Equilateral triangle
(iv)
Obtuse angled triangle
Question
50
50.
EFGH is a rhombus. N, O, P and Q are mid-points of sides EF, FG, GH and HE. Find ∠OPQ
(i)
88°
(ii)
90°
(iii)
89°
(iv)
91°
(v)
92°
Question
51
51.
In the given figure, EFGH is a parallelogram such that S is the mid-point of EF and EF = 2HE. Find ∠HSG
(i)
88°
(ii)
91°
(iii)
92°
(iv)
90°
(v)
89°
Question
52
52.
IJKL is an isosceles trapezium. IR and JR are angular bisector of ∠I & ∠J. If ∠I = 67°, find ∠IRJ
(i)
111°
(ii)
115°
(iii)
112°
(iv)
114°
(v)
113°
Question
53
53.
In the given figure, BCDE is a parallelogram. The bisector of the angles B, C, D & E intersect at Q, R, S & T to form a quadrilateral. Find ∠QRS
(i)
92°
(ii)
90°
(iii)
91°
(iv)
88°
(v)
89°
Assignment Key
1) (iii)
2) (iii)
3) (ii)
4) (iii)
5) (ii)
6) (iii)
7) (v)
8) (iv)
9) (iv)
10) (i)
11) (iv)
12) (v)
13) (iv)
14) (i)
15) (ii)
16) (iv)
17) (ii)
18) (ii)
19) (iii)
20) (iii)
21) (v)
22) (ii)
23) (iii)
24) (v)
25) (v)
26) (iii)
27) (ii)
28) (iii)
29) (iii)
30) (iv)
31) (ii)
32) (iii)
33) (v)
34) (ii)
35) (iv)
36) (ii)
37) (i)
38) (iii)
39) (ii)
40) (iii)
41) (ii)
42) (ii)
43) (v)
44) (ii)
45) (ii)
46) (i)
47) (v)
48) (v)
49) (iii)
50) (ii)
51) (iv)
52) (v)
53) (ii)
