EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
In parallelogram ABCD, if ∠B = 153.66°, then find the value of ∠A
(i)
26.34°
(ii)
25.34°
(iii)
24.34°
(iv)
28.34°
(v)
27.34°
Question
2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
88°
(ii)
90°
(iii)
92°
(iv)
89°
(v)
91°
Question
3
3.
The sum of the interior angles of a quadrilateral is
(i)
180°
(ii)
360°
(iii)
270°
(iv)
90°
Question
4
4.
If ABCD is an isosceles trapezium, ∠B =
(i)
∠D
(ii)
∠C
(iii)
∠A
(iv)
90°
Question
5
5.
BCDE is a rhombus in which ∠B = 120° .
CE
is the diagonal. Then △BCD is
(i)
an isosceles triangle
(ii)
an equilateral triangle
(iii)
a scalene triangle
(iv)
None of these
(v)
an obtuse angled triangle
Question
6
6.
JKLM is a rhombus in which ∠J = 92° .
KM
is the diagonal. Then △JKL is
(i)
None of these
(ii)
an isosceles triangle
(iii)
an obtuse angled triangle
(iv)
a scalene triangle
(v)
an equilateral triangle
Question
7
7.
The angles of a quadrilateral NOPQ are in the ratio 19 : 27 : 44 : 90. Find the measure of each angle of the quadrilateral.
(i)
N
=
36°
,
O
=
56°
,
P
=
87°
,
Q
=
181°
(ii)
N
=
38°
,
O
=
54°
,
P
=
88°
,
Q
=
180°
(iii)
N
=
39°
,
O
=
53°
,
P
=
90°
,
Q
=
178°
(iv)
N
=
40°
,
O
=
53°
,
P
=
86°
,
Q
=
181°
(v)
N
=
37°
,
O
=
52°
,
P
=
89°
,
Q
=
182°
Question
8
8.
Two adjacent angles of a parallelogram ABCD are in the ratio 10 : 10. Find the measure of each of its angles.
(i)
A
=
90°
,
B
=
90°
,
C
=
90°
,
D
=
90°
(ii)
A
=
91°
,
B
=
89°
,
C
=
92°
,
D
=
88°
(iii)
A
=
88°
,
B
=
92°
,
C
=
89°
,
D
=
91°
(iv)
A
=
92°
,
B
=
89°
,
C
=
88°
,
D
=
91°
(v)
A
=
89°
,
B
=
88°
,
C
=
91°
,
D
=
92°
Question
9
9.
In the adjoining figure,
DEFG
is a parallelogram in which
∠GDF = 55.84°
,
∠FDE = 64.8°
,
∠GHF = 84.22°
. Calculate
∠DEG
(i)
32.98°
(ii)
31.98°
(iii)
29.98°
(iv)
28.98°
(v)
30.98°
Question
10
10.
In the adjoining figure,
ABCD
is a parallelogram in which
∠DAC = 27.46°
,
∠CAB = 24.38°
,
∠DEC = 98.18°
. Calculate
∠CDB
(i)
56.44°
(ii)
59.44°
(iii)
58.44°
(iv)
57.44°
(v)
55.44°
Question
11
11.
In the adjoining figure,
LMNO
is a parallelogram in which
∠OLN = 21.43°
,
∠NLM = 13.59°
,
∠OPN = 126.58°
. Calculate
∠MNL
(i)
22.43°
(ii)
23.43°
(iii)
19.43°
(iv)
20.43°
(v)
21.43°
Question
12
12.
In the adjoining figure,
CDEF
is a parallelogram in which
∠FCE = 27.43°
,
∠ECD = 22.68°
,
∠FGE = 103.12°
. Calculate
∠FDE
(i)
77.70°
(ii)
76.70°
(iii)
73.70°
(iv)
75.70°
(v)
74.70°
Question
13
13.
In the adjoining figure,
JKLM
is a rectangle.
If
∠LJK = 49.64°
, find
∠MNL
(i)
82.72°
(ii)
78.72°
(iii)
80.72°
(iv)
81.72°
(v)
79.72°
Question
14
14.
Three angles of quadrilateral measure 68.78°, 49.14° and 103.14° respectively. Find the measure of the fourth angle
(i)
136.94°
(ii)
140.94°
(iii)
138.94°
(iv)
137.94°
(v)
139.94°
Question
15
15.
Three angles of a quadrilateral are equal and the fourth angle measure 54.77°. What is the measure of each of the equal angles?
(i)
101.74°
(ii)
102.74°
(iii)
100.74°
(iv)
103.74°
(v)
99.74°
Question
16
16.
Two angles of a quadrilateral are of measure 115.37° and 89.17° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
75.73°
(ii)
77.73°
(iii)
76.73°
(iv)
78.73°
(v)
79.73°
Question
17
17.
A quadrilateral has three acute angles, each measuring 47°. What is the measure of its fourth angle?
(i)
218.00°
(ii)
221.00°
(iii)
219.00°
(iv)
217.00°
(v)
220.00°
Question
18
18.
One angle of a parallelogram measures
I
=
58.67°
.
Find the measure of each of its remaining angles.
(i)
J
=
120.33°
,
K
=
57.67°
,
L
=
120.33°
(ii)
J
=
123.33°
,
K
=
60.67°
,
L
=
123.33°
(iii)
J
=
122.33°
,
K
=
59.67°
,
L
=
122.33°
(iv)
J
=
119.33°
,
K
=
56.67°
,
L
=
119.33°
(v)
J
=
121.33°
,
K
=
58.67°
,
L
=
121.33°
Question
19
19.
Two adjacent angles of a parallelogram are in the ratio
4 : 26
.
Find the measure of each of its angles.
(i)
A
=
23°
,
B
=
154°
,
C
=
25°
,
D
=
158°
(ii)
A
=
26°
,
B
=
155°
,
C
=
22°
,
D
=
157°
(iii)
A
=
24°
,
B
=
156°
,
C
=
24°
,
D
=
156°
(iv)
A
=
22°
,
B
=
158°
,
C
=
23°
,
D
=
157°
(v)
A
=
25°
,
B
=
155°
,
C
=
26°
,
D
=
154°
Question
20
20.
In the figure given below,
PQRS
is a rectangle.
Find the values of x and y
(i)
x
=
64.24°
,
y
=
126.48°
(ii)
x
=
62.24°
,
y
=
124.48°
(iii)
x
=
63.24°
,
y
=
125.48°
(iv)
x
=
61.24°
,
y
=
123.48°
(v)
x
=
60.24°
,
y
=
122.48°
Question
21
21.
In the figure given below,
HIJK
is a rectangle.
Find the values of x and y
(i)
x
=
41.51°
,
y
=
46.49°
(ii)
x
=
43.51°
,
y
=
48.49°
(iii)
x
=
40.51°
,
y
=
45.49°
(iv)
x
=
42.51°
,
y
=
47.49°
(v)
x
=
44.51°
,
y
=
49.49°
Question
22
22.
In the figure given below,
OPQR
is a rhombus.
Find the values of x and y
(i)
x
=
55.13°
,
y
=
55.13°
(ii)
x
=
51.13°
,
y
=
51.13°
(iii)
x
=
54.13°
,
y
=
54.13°
(iv)
x
=
53.13°
,
y
=
53.13°
(v)
x
=
52.13°
,
y
=
52.13°
Question
23
23.
In the figure given below,
PQRS
is a rhombus.
Find the values of x and y
(i)
x
=
29.89°
,
y
=
29.89°
(ii)
x
=
31.89°
,
y
=
31.89°
(iii)
x
=
30.89°
,
y
=
30.89°
(iv)
x
=
32.89°
,
y
=
32.89°
(v)
x
=
33.89°
,
y
=
33.89°
Question
24
24.
In the figure given below,
FGHI
is a rhombus.
Find the values of x and y
(i)
x
=
18.43°
,
y
=
71.57°
(ii)
x
=
16.43°
,
y
=
69.57°
(iii)
x
=
19.43°
,
y
=
72.57°
(iv)
x
=
20.43°
,
y
=
73.57°
(v)
x
=
17.43°
,
y
=
70.57°
Question
25
25.
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
=
58°
,
E
=
122°
,
F
=
59°
,
G
=
121°
(iii)
D
=
60°
,
E
=
120°
,
F
=
60°
,
G
=
120°
(iv)
D
=
62°
,
E
=
119°
,
F
=
58°
,
G
=
121°
(v)
D
=
61°
,
E
=
119°
,
F
=
62°
,
G
=
118°
Question
26
26.
In the adjoining figure,
FGHI
is a trapezium in which
FG
∥
HI
.
If
x = 50.65°
and
y = 74.36°
,
find the measures of
∠H
and
∠I
.
(i)
H
=
105.64°
,
I
=
129.35°
(ii)
H
=
104.64°
,
I
=
128.35°
(iii)
H
=
103.64°
,
I
=
127.35°
(iv)
H
=
107.64°
,
I
=
131.35°
(v)
H
=
106.64°
,
I
=
130.35°
Question
27
27.
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 = 51.62° and ∠ABO = 60.95°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 38.38° , b = 30.05° , c = 60.95° , d = 38.38° , e = 51.62°
(ii)
a = 38.38° , b = 30.05° , c = 59.95° , d = 38.38° , e = 51.62°
(iii)
a = 38.38° , b = 30.05° , c = 59.95° , d = 40.38° , e = 51.62°
(iv)
a = 38.38° , b = 29.05° , c = 60.95° , d = 38.38° , e = 51.62°
(v)
a = 38.38° , b = 30.05° , c = 59.95° , d = 40.38° , e = 49.62°
Question
28
28.
In the adjoining figure, side KL of parallelogram IJKL has been produced to M. If ∠ILM = 45.81° , find the measure of each angle of the parallelogram.
(i)
I
=
43.81°
,
J
=
136.19°
,
K
=
44.81°
,
L
=
135.19°
(ii)
I
=
46.81°
,
J
=
133.19°
,
K
=
47.81°
,
L
=
132.19°
(iii)
I
=
45.81°
,
J
=
134.19°
,
K
=
45.81°
,
L
=
134.19°
(iv)
I
=
47.81°
,
J
=
133.19°
,
K
=
43.81°
,
L
=
135.19°
(v)
I
=
44.81°
,
J
=
132.19°
,
K
=
46.81°
,
L
=
136.19°
Question
29
29.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
4 : 6
,
find the angles of
△OAB
.
(i)
O
=
92°
,
A
=
36°
,
B
=
52°
(ii)
O
=
88°
,
A
=
38°
,
B
=
54°
(iii)
O
=
90°
,
A
=
36°
,
B
=
54°
(iv)
O
=
90°
,
A
=
34°
,
B
=
56°
(v)
O
=
88°
,
A
=
36°
,
B
=
56°
Question
30
30.
In the given figure,
ABCD
is a rectangle whose diagonals intersect at
E
.
Diagonal
AC
is produced to
T
and
∠BAT =
132.71°
. Find the angles of
△ECD
.
(i)
E
=
85.42°
,
C
=
45.29°
,
D
=
49.29°
(ii)
E
=
85.42°
,
C
=
47.29°
,
D
=
47.29°
(iii)
E
=
87.42°
,
C
=
47.29°
,
D
=
45.29°
(iv)
E
=
83.42°
,
C
=
49.29°
,
D
=
47.29°
(v)
E
=
83.42°
,
C
=
47.29°
,
D
=
49.29°
Question
31
31.
The measures of three angles of a quadrilateral are
59.3°
,
137.36°
and
59.3°
. Find the fourth angle
(i)
119.04°
(ii)
104.04°
(iii)
134.04°
(iv)
109.04°
(v)
114.04°
Question
32
32.
Find the missing angle in the given quadrilateral
(i)
76.23°
(ii)
61.23°
(iii)
71.23°
(iv)
91.23°
(v)
66.23°
Question
33
33.
Find the missing angle in the given trapezium
(i)
133.76°
(ii)
103.76°
(iii)
118.76°
(iv)
113.76°
(v)
108.76°
Question
34
34.
Find the missing angle in the given parallelogram
(i)
127.73°
(ii)
132.73°
(iii)
152.73°
(iv)
137.73°
(v)
122.73°
Question
35
35.
Find the missing angle in the given rhombus
(i)
117.57°
(ii)
107.57°
(iii)
132.57°
(iv)
112.57°
(v)
102.57°
Question
36
36.
In the given figure, HIJK is a parallelogram.
If
HR
and
IR
are bisector of
∠H
&
∠I
, find
∠R
(i)
92°
(ii)
91°
(iii)
89°
(iv)
90°
(v)
88°
Question
37
37.
In the given figure, FGHI is a parallelogram. T is the mid-point of HI.
GT
bisects
∠G
. If x =
53°
, find angle 'y'.
(i)
37°
(ii)
36°
(iii)
35°
(iv)
39°
(v)
38°
Question
38
38.
In the given figure, BCDE is a quadrilateral. RE and RD are bisectors of ∠E & ∠D meeting at R. Find ∠DRE
(i)
92.0°
(ii)
88.0°
(iii)
90.0°
(iv)
89.0°
(v)
91.0°
Question
39
39.
In the given figure, CDEF is a rhombus. Given x = 56°, find the value of 'y'.
(i)
35°
(ii)
36°
(iii)
34°
(iv)
32°
(v)
33°
Question
40
40.
In the given figure, DEFG is a parallelogram. DF bisects ∠D & ∠F.
Given
DF = 9 cm
and
EG = 6 cm
, find
DE
(i)
3.41 cm
(ii)
5.41 cm
(iii)
4.41 cm
(iv)
6.41 cm
(v)
7.41 cm
Question
41
41.
In the given figure, JKLM is a parallelogram. KM is the diagonal
such that
JM = KM = KL
. Given
∠J = 64°
, find
∠MKL
(i)
53°
(ii)
52°
(iii)
50°
(iv)
51°
(v)
54°
Question
42
42.
In the given figure, EFGH is a parallelogram. EQ and GR are perpendicular to the diagonal FH. Given ∠QEF = 16°, find ∠GHF
(i)
75°
(ii)
76°
(iii)
74°
(iv)
73°
(v)
72°
Question
43
43.
In the given figure, FGHI is a rhombus such that ∠G = 120°. Then △FGI is
(i)
Obtuse angled triangle
(ii)
Isosceles triangle
(iii)
Right angled triangle
(iv)
Equilateral triangle
Question
44
44.
BCDE is a rhombus. M, N, O and P are mid-points of sides BC, CD, DE and EB. Find ∠NOP
(i)
90°
(ii)
88°
(iii)
92°
(iv)
89°
(v)
91°
Question
45
45.
In the given figure, EFGH is a parallelogram such that T is the mid-point of EF and EF = 2HE. Find ∠HTG
(i)
92°
(ii)
89°
(iii)
91°
(iv)
88°
(v)
90°
Question
46
46.
BCDE is an isosceles trapezium. BS and CS are angular bisector of ∠B & ∠C. If ∠B = 64°, find ∠BSC
(i)
117°
(ii)
118°
(iii)
115°
(iv)
116°
(v)
114°
Question
47
47.
In the given figure, ABCD is a parallelogram. The bisector of the angles A, B, C & D intersect at S, T, U & V to form a quadrilateral. Find ∠UVS
(i)
89°
(ii)
91°
(iii)
88°
(iv)
90°
(v)
92°
Assignment Key
1) (i)
2) (ii)
3) (ii)
4) (iii)
5) (ii)
6) (ii)
7) (ii)
8) (i)
9) (v)
10) (iv)
11) (v)
12) (iv)
13) (iii)
14) (iii)
15) (i)
16) (ii)
17) (iii)
18) (v)
19) (iii)
20) (ii)
21) (iv)
22) (iv)
23) (ii)
24) (i)
25) (iii)
26) (i)
27) (iv)
28) (iii)
29) (iii)
30) (ii)
31) (ii)
32) (ii)
33) (ii)
34) (v)
35) (v)
36) (iv)
37) (i)
38) (iii)
39) (iii)
40) (ii)
41) (ii)
42) (iii)
43) (iv)
44) (i)
45) (v)
46) (iv)
47) (iv)
