EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Understanding Quadrilaterals
Grade : CBSE Grade VIII
License : Non Commercial Use
Question
1
1.
The measures of three angles of a quadrilateral are
72.44°
,
113.78°
and
60°
. Find the fourth angle
(i)
128.78°
(ii)
123.78°
(iii)
113.78°
(iv)
118.78°
(v)
143.78°
Question
2
2.
Sum of the interior angles in a quadrilateral is
(i)
390°
(ii)
370°
(iii)
375°
(iv)
365°
(v)
360°
Question
3
3.
Find the missing angle in the given quadrilateral
(i)
64.33°
(ii)
59.33°
(iii)
74.33°
(iv)
89.33°
(v)
69.33°
Question
4
4.
Find the missing angle in the given trapezium
(i)
106.13°
(ii)
111.13°
(iii)
136.13°
(iv)
121.13°
(v)
116.13°
Question
5
5.
Find the missing angle in the given parallelogram
(i)
136.87°
(ii)
141.87°
(iii)
156.87°
(iv)
131.87°
(v)
126.87°
Question
6
6.
Find the missing angle in the given rhombus
(i)
77.64°
(ii)
67.64°
(iii)
72.64°
(iv)
97.64°
(v)
82.64°
Question
7
7.
In parallelogram ABCD, if ∠C = 80.28°, then find the value of ∠A
(i)
82.28°
(ii)
79.28°
(iii)
78.28°
(iv)
80.28°
(v)
81.28°
Question
8
8.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
88°
(ii)
90°
(iii)
91°
(iv)
92°
(v)
89°
Question
9
9.
If ABCD is an isosceles trapezium, ∠A =
(i)
∠C
(ii)
∠D
(iii)
∠B
(iv)
90°
Question
10
10.
KLMN is a rhombus in which ∠K = 120° .
LN
is the diagonal. Then △KLM is
(i)
an equilateral triangle
(ii)
an isosceles triangle
(iii)
a scalene triangle
(iv)
an obtuse angled triangle
(v)
None of these
Question
11
11.
NOPQ is a rhombus in which ∠N = 83° .
OQ
is the diagonal. Then △NOP is
(i)
an equilateral triangle
(ii)
an obtuse angled triangle
(iii)
an isosceles triangle
(iv)
None of these
(v)
a scalene triangle
Question
12
12.
The angles of a quadrilateral KLMN are in the ratio 13 : 10 : 11 : 26. Find the measure of each angle of the quadrilateral.
(i)
K
=
80°
,
L
=
59°
,
M
=
64°
,
N
=
157°
(ii)
K
=
79°
,
L
=
59°
,
M
=
68°
,
N
=
154°
(iii)
K
=
78°
,
L
=
60°
,
M
=
66°
,
N
=
156°
(iv)
K
=
77°
,
L
=
58°
,
M
=
67°
,
N
=
158°
(v)
K
=
76°
,
L
=
62°
,
M
=
65°
,
N
=
157°
Question
13
13.
Two adjacent angles of a parallelogram LMNO are in the ratio 28 : 32. Find the measure of each of its angles.
(i)
L
=
84°
,
M
=
96°
,
N
=
84°
,
O
=
96°
(ii)
L
=
82°
,
M
=
98°
,
N
=
83°
,
O
=
97°
(iii)
L
=
85°
,
M
=
95°
,
N
=
86°
,
O
=
94°
(iv)
L
=
83°
,
M
=
94°
,
N
=
85°
,
O
=
98°
(v)
L
=
86°
,
M
=
95°
,
N
=
82°
,
O
=
97°
Question
14
14.
In the adjoining figure,
CDEF
is a parallelogram in which
∠FCE = 20.94°
,
∠ECD = 42.09°
,
∠FGE = 52.28°
. Calculate
∠CDF
(i)
85.63°
(ii)
84.63°
(iii)
83.63°
(iv)
86.63°
(v)
87.63°
Question
15
15.
In the adjoining figure,
PQRS
is a parallelogram in which
∠SPR = 17.74°
,
∠RPQ = 15.75°
,
∠STR = 101.94°
. Calculate
∠RSQ
(i)
61.31°
(ii)
62.31°
(iii)
64.31°
(iv)
63.31°
(v)
60.31°
Question
16
16.
In the adjoining figure,
KLMN
is a parallelogram in which
∠NKM = 36.11°
,
∠MKL = 50.81°
,
∠NOM = 75.01°
. Calculate
∠LMK
(i)
37.11°
(ii)
35.11°
(iii)
36.11°
(iv)
34.11°
(v)
38.11°
Question
17
17.
In the adjoining figure,
GHIJ
is a parallelogram in which
∠JGI = 20.16°
,
∠IGH = 18.78°
,
∠JKI = 94.32°
. Calculate
∠JHI
(i)
73.16°
(ii)
76.16°
(iii)
75.16°
(iv)
72.16°
(v)
74.16°
Question
18
18.
In the adjoining figure,
FGHI
is a rectangle.
If
∠HFG = 48.01°
, find
∠GHF
(i)
43.99°
(ii)
39.99°
(iii)
42.99°
(iv)
40.99°
(v)
41.99°
Question
19
19.
Three angles of quadrilateral measure 62.18°, 97.18° and 103.59° respectively. Find the measure of the fourth angle
(i)
99.05°
(ii)
95.05°
(iii)
96.05°
(iv)
97.05°
(v)
98.05°
Question
20
20.
Three angles of a quadrilateral are equal and the fourth angle measure 28.96°. What is the measure of each of the equal angles?
(i)
109.35°
(ii)
112.35°
(iii)
108.35°
(iv)
111.35°
(v)
110.35°
Question
21
21.
Two angles of a quadrilateral are of measure 66.87° and 83.76° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
106.69°
(ii)
103.69°
(iii)
105.69°
(iv)
104.69°
(v)
102.69°
Question
22
22.
A quadrilateral has three acute angles, each measuring 52°. What is the measure of its fourth angle?
(i)
206.00°
(ii)
205.00°
(iii)
203.00°
(iv)
204.00°
(v)
202.00°
Question
23
23.
One angle of a parallelogram measures
A
=
74.85°
.
Find the measure of each of its remaining angles.
(i)
B
=
104.15°
,
C
=
73.85°
,
D
=
104.15°
(ii)
B
=
107.15°
,
C
=
76.85°
,
D
=
107.15°
(iii)
B
=
105.15°
,
C
=
74.85°
,
D
=
105.15°
(iv)
B
=
106.15°
,
C
=
75.85°
,
D
=
106.15°
(v)
B
=
103.15°
,
C
=
72.85°
,
D
=
103.15°
Question
24
24.
Two adjacent angles of a parallelogram are in the ratio
5 : 5
.
Find the measure of each of its angles.
(i)
A
=
88°
,
B
=
92°
,
C
=
89°
,
D
=
91°
(ii)
A
=
90°
,
B
=
90°
,
C
=
90°
,
D
=
90°
(iii)
A
=
91°
,
B
=
89°
,
C
=
92°
,
D
=
88°
(iv)
A
=
89°
,
B
=
88°
,
C
=
91°
,
D
=
92°
(v)
A
=
92°
,
B
=
89°
,
C
=
88°
,
D
=
91°
Question
25
25.
In the figure given below,
IJKL
is a rectangle.
Find the values of x and y
(i)
x
=
59.72°
,
y
=
117.44°
(ii)
x
=
55.72°
,
y
=
113.44°
(iii)
x
=
56.72°
,
y
=
114.44°
(iv)
x
=
58.72°
,
y
=
116.44°
(v)
x
=
57.72°
,
y
=
115.44°
Question
26
26.
In the figure given below,
DEFG
is a rectangle.
Find the values of x and y
(i)
x
=
57.09°
,
y
=
32.91°
(ii)
x
=
59.09°
,
y
=
34.91°
(iii)
x
=
55.09°
,
y
=
30.91°
(iv)
x
=
56.09°
,
y
=
31.91°
(v)
x
=
58.09°
,
y
=
33.91°
Question
27
27.
In the figure given below,
GHIJ
is a rhombus.
Find the values of x and y
(i)
x
=
24.35°
,
y
=
24.35°
(ii)
x
=
21.35°
,
y
=
21.35°
(iii)
x
=
22.35°
,
y
=
22.35°
(iv)
x
=
23.35°
,
y
=
23.35°
(v)
x
=
25.35°
,
y
=
25.35°
Question
28
28.
In the figure given below,
ABCD
is a rhombus.
Find the values of x and y
(i)
x
=
49.18°
,
y
=
49.18°
(ii)
x
=
48.18°
,
y
=
48.18°
(iii)
x
=
46.18°
,
y
=
46.18°
(iv)
x
=
47.18°
,
y
=
47.18°
(v)
x
=
50.18°
,
y
=
50.18°
Question
29
29.
In the figure given below,
HIJK
is a rhombus.
Find the values of x and y
(i)
x
=
37.29°
,
y
=
54.71°
(ii)
x
=
38.29°
,
y
=
55.71°
(iii)
x
=
35.29°
,
y
=
52.71°
(iv)
x
=
36.29°
,
y
=
53.71°
(v)
x
=
34.29°
,
y
=
51.71°
Question
30
30.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
H
=
62°
,
I
=
119°
,
J
=
58°
,
K
=
121°
(ii)
H
=
59°
,
I
=
118°
,
J
=
61°
,
K
=
122°
(iii)
H
=
58°
,
I
=
122°
,
J
=
59°
,
K
=
121°
(iv)
H
=
61°
,
I
=
119°
,
J
=
62°
,
K
=
118°
(v)
H
=
60°
,
I
=
120°
,
J
=
60°
,
K
=
120°
Question
31
31.
In the adjoining figure,
LMNO
is a trapezium in which
LM
∥
NO
.
If
x = 99.78°
and
y = 117.35°
,
find the measures of
∠L
and
∠M
.
(i)
L
=
62.65°
,
M
=
80.22°
(ii)
L
=
64.65°
,
M
=
82.22°
(iii)
L
=
60.65°
,
M
=
78.22°
(iv)
L
=
61.65°
,
M
=
79.22°
(v)
L
=
63.65°
,
M
=
81.22°
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 = 26.28° and ∠ABO = 58.39°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 63.72° , b = 32.61° , c = 58.39° , d = 63.72° , e = 26.28°
(ii)
a = 63.72° , b = 32.61° , c = 57.39° , d = 65.72° , e = 24.28°
(iii)
a = 63.72° , b = 32.61° , c = 57.39° , d = 63.72° , e = 26.28°
(iv)
a = 63.72° , b = 31.61° , c = 58.39° , d = 63.72° , e = 26.28°
(v)
a = 63.72° , b = 32.61° , c = 57.39° , d = 65.72° , e = 26.28°
Question
33
33.
In the adjoining figure, side KH of parallelogram HIJK has been produced to L. If ∠IHL = 119.53° , find the measure of each angle of the parallelogram.
(i)
H
=
60.47°
,
I
=
119.53°
,
J
=
60.47°
,
K
=
119.53°
(ii)
H
=
61.47°
,
I
=
118.53°
,
J
=
62.47°
,
K
=
117.53°
(iii)
H
=
59.47°
,
I
=
117.53°
,
J
=
61.47°
,
K
=
121.53°
(iv)
H
=
58.47°
,
I
=
121.53°
,
J
=
59.47°
,
K
=
120.53°
(v)
H
=
62.47°
,
I
=
118.53°
,
J
=
58.47°
,
K
=
120.53°
Question
34
34.
In the adjoining figure,
KLMN
is a parallelogram and
OP
is such that
OP
∥
KM
If
∠KNO = 24.66°
and
∠MNP = 26.86°
,
find the measure of
∠MNK
.
(i)
130.48°
(ii)
127.48°
(iii)
128.48°
(iv)
129.48°
(v)
126.48°
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 = 94.81° and ∠TUR = x°. Find the value of x .
(i)
50.81°
(ii)
49.81°
(iii)
48.81°
(iv)
47.81°
(v)
51.81°
Question
36
36.
In the adjoining figure, NOPQ is a rhombus and △RQP is an equilateral triangle. R and O are on opposite sides of PQ. If ∠QNO = 73.74°, find the values of x and y .
(i)
x
=
29°
,
y
=
22.13°
(ii)
x
=
32°
,
y
=
25.13°
(iii)
x
=
28°
,
y
=
21.13°
(iv)
x
=
31°
,
y
=
24.13°
(v)
x
=
30°
,
y
=
23.13°
Question
37
37.
In the adjoining figure, equilateral △EDF surmounts square BCDE. If DFB = x°, find the value of x.
(i)
44°
(ii)
47°
(iii)
45°
(iv)
43°
(v)
46°
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
=
88°
,
A
=
47°
,
B
=
45°
(iv)
O
=
90°
,
A
=
45°
,
B
=
45°
(v)
O
=
90°
,
A
=
43°
,
B
=
47°
Question
39
39.
In the given figure,
GHIJ
is a rectangle whose diagonals intersect at
K
.
Diagonal
GI
is produced to
T
and
∠HGT =
136.73°
. Find the angles of
△KJG
.
(i)
K
=
84.53°
,
J
=
46.74°
,
G
=
48.73°
(ii)
K
=
86.53°
,
J
=
44.74°
,
G
=
48.73°
(iii)
K
=
88.53°
,
J
=
46.74°
,
G
=
44.73°
(iv)
K
=
86.53°
,
J
=
46.74°
,
G
=
46.73°
(v)
K
=
84.53°
,
J
=
48.74°
,
G
=
46.73°
Question
40
40.
In the given figure,
LMNO
is a kite whose diagonals intersect at
P
.
If
∠OLM = 60.93°
and
∠LMN = 127.96°
, calculate
∠POL
and
∠PNO
.
(i)
x
=
58.53°
,
y
=
20.58°
(ii)
x
=
60.53°
,
y
=
22.58°
(iii)
x
=
59.53°
,
y
=
21.58°
(iv)
x
=
57.53°
,
y
=
19.58°
(v)
x
=
61.53°
,
y
=
23.58°
Question
41
41.
△IFG
is an equilateral triangle in a square
EFGH
.
If
FH
and
GI
intersect at
J
,
then find the value of x.
(i)
76°
(ii)
77°
(iii)
74°
(iv)
73°
(v)
75°
Question
42
42.
In the adjoining figure,
I
is a point in the interior of
∠KGL
.
If
IH
⟂
GK
and
IJ
⟂
GL
and
∠KGL = 41°
,
find the measure of x .
(i)
140°
(ii)
141°
(iii)
138°
(iv)
137°
(v)
139°
Assignment Key
1) (iii)
2) (v)
3) (ii)
4) (i)
5) (v)
6) (ii)
7) (iv)
8) (ii)
9) (iii)
10) (i)
11) (iii)
12) (iii)
13) (i)
14) (i)
15) (ii)
16) (iii)
17) (v)
18) (v)
19) (iv)
20) (v)
21) (iv)
22) (iv)
23) (iii)
24) (ii)
25) (v)
26) (i)
27) (iv)
28) (ii)
29) (iv)
30) (v)
31) (i)
32) (iv)
33) (i)
34) (iii)
35) (ii)
36) (v)
37) (iii)
38) (iv)
39) (iv)
40) (iii)
41) (v)
42) (v)
