EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade VII
License : Non Commercial Use
Question
1
1.
In parallelogram ABCD, if ∠D = 75.53°, then find the value of ∠A
(i)
104.47°
(ii)
106.47°
(iii)
103.47°
(iv)
105.47°
(v)
102.47°
Question
2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
88°
(ii)
92°
(iii)
89°
(iv)
91°
(v)
90°
Question
3
3.
The sum of the interior angles of a quadrilateral is
(i)
270°
(ii)
360°
(iii)
90°
(iv)
180°
Question
4
4.
If ABCD is an isosceles trapezium, ∠B =
(i)
∠A
(ii)
∠C
(iii)
90°
(iv)
∠D
Question
5
5.
KLMN is a rhombus in which ∠K = 120° .
LN
is the diagonal. Then △KLM is
(i)
an equilateral triangle
(ii)
an obtuse angled triangle
(iii)
an isosceles triangle
(iv)
a scalene triangle
(v)
None of these
Question
6
6.
HIJK is a rhombus in which ∠H = 113° .
IK
is the diagonal. Then △HIJ is
(i)
None of these
(ii)
a scalene triangle
(iii)
an isosceles triangle
(iv)
an equilateral triangle
(v)
an obtuse angled triangle
Question
7
7.
The angles of a quadrilateral IJKL are in the ratio 1 : 2 : 3 : 6. Find the measure of each angle of the quadrilateral.
(i)
I
=
32°
,
J
=
59°
,
K
=
88°
,
L
=
181°
(ii)
I
=
29°
,
J
=
58°
,
K
=
91°
,
L
=
182°
(iii)
I
=
30°
,
J
=
60°
,
K
=
90°
,
L
=
180°
(iv)
I
=
28°
,
J
=
62°
,
K
=
89°
,
L
=
181°
(v)
I
=
31°
,
J
=
59°
,
K
=
92°
,
L
=
178°
Question
8
8.
Two adjacent angles of a parallelogram BCDE are in the ratio 7 : 13. Find the measure of each of its angles.
(i)
B
=
65°
,
C
=
116°
,
D
=
61°
,
E
=
118°
(ii)
B
=
64°
,
C
=
116°
,
D
=
65°
,
E
=
115°
(iii)
B
=
63°
,
C
=
117°
,
D
=
63°
,
E
=
117°
(iv)
B
=
62°
,
C
=
115°
,
D
=
64°
,
E
=
119°
(v)
B
=
61°
,
C
=
119°
,
D
=
62°
,
E
=
118°
Question
9
9.
In the adjoining figure,
MNOP
is a parallelogram in which
∠PMO = 22.65°
,
∠OMN = 46.33°
,
∠PQO = 53.54°
. Calculate
∠MNP
(i)
81.13°
(ii)
78.13°
(iii)
82.13°
(iv)
79.13°
(v)
80.13°
Question
10
10.
In the adjoining figure,
LMNO
is a parallelogram in which
∠OLN = 23.41°
,
∠NLM = 24.58°
,
∠OPN = 85.36°
. Calculate
∠NOM
(i)
72.06°
(ii)
69.06°
(iii)
68.06°
(iv)
70.06°
(v)
71.06°
Question
11
11.
In the adjoining figure,
ABCD
is a parallelogram in which
∠DAC = 12.38°
,
∠CAB = 16.5°
,
∠DEC = 59.46°
. Calculate
∠BCA
(i)
13.38°
(ii)
14.38°
(iii)
12.38°
(iv)
10.38°
(v)
11.38°
Question
12
12.
In the adjoining figure,
NOPQ
is a parallelogram in which
∠QNP = 25.49°
,
∠PNO = 21.43°
,
∠QRP = 102.68°
. Calculate
∠QOP
(i)
78.20°
(ii)
77.20°
(iii)
79.20°
(iv)
76.20°
(v)
75.20°
Question
13
13.
In the adjoining figure,
MNOP
is a rectangle.
If
∠OMN = 53.13°
, find
∠MNP
(i)
54.13°
(ii)
51.13°
(iii)
52.13°
(iv)
53.13°
(v)
55.13°
Question
14
14.
Three angles of quadrilateral measure 67.15°, 141.04° and 76.5° respectively. Find the measure of the fourth angle
(i)
75.31°
(ii)
76.31°
(iii)
77.31°
(iv)
74.31°
(v)
73.31°
Question
15
15.
Three angles of a quadrilateral are equal and the fourth angle measure 132.17°. What is the measure of each of the equal angles?
(i)
77.94°
(ii)
73.94°
(iii)
75.94°
(iv)
74.94°
(v)
76.94°
Question
16
16.
Two angles of a quadrilateral are of measure 75.52° and 111.78° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
85.35°
(ii)
86.35°
(iii)
87.35°
(iv)
88.35°
(v)
84.35°
Question
17
17.
A quadrilateral has three acute angles, each measuring 77°. What is the measure of its fourth angle?
(i)
128.00°
(ii)
127.00°
(iii)
129.00°
(iv)
130.00°
(v)
131.00°
Question
18
18.
One angle of a parallelogram measures
O
=
85.46°
.
Find the measure of each of its remaining angles.
(i)
P
=
94.54°
,
Q
=
85.46°
,
R
=
94.54°
(ii)
P
=
92.54°
,
Q
=
83.46°
,
R
=
92.54°
(iii)
P
=
95.54°
,
Q
=
86.46°
,
R
=
95.54°
(iv)
P
=
96.54°
,
Q
=
87.46°
,
R
=
96.54°
(v)
P
=
93.54°
,
Q
=
84.46°
,
R
=
93.54°
Question
19
19.
Two adjacent angles of a parallelogram are in the ratio
11 : 25
.
Find the measure of each of its angles.
(i)
A
=
55°
,
B
=
125°
,
C
=
55°
,
D
=
125°
(ii)
A
=
57°
,
B
=
124°
,
C
=
53°
,
D
=
126°
(iii)
A
=
53°
,
B
=
127°
,
C
=
54°
,
D
=
126°
(iv)
A
=
54°
,
B
=
123°
,
C
=
56°
,
D
=
127°
(v)
A
=
56°
,
B
=
124°
,
C
=
57°
,
D
=
123°
Question
20
20.
In the figure given below,
OPQR
is a rectangle.
Find the values of x and y
(i)
x
=
51.62°
,
y
=
105.24°
(ii)
x
=
55.62°
,
y
=
109.24°
(iii)
x
=
53.62°
,
y
=
107.24°
(iv)
x
=
54.62°
,
y
=
108.24°
(v)
x
=
52.62°
,
y
=
106.24°
Question
21
21.
In the figure given below,
MNOP
is a rectangle.
Find the values of x and y
(i)
x
=
53.49°
,
y
=
32.51°
(ii)
x
=
57.49°
,
y
=
36.51°
(iii)
x
=
56.49°
,
y
=
35.51°
(iv)
x
=
55.49°
,
y
=
34.51°
(v)
x
=
54.49°
,
y
=
33.51°
Question
22
22.
In the figure given below,
DEFG
is a rhombus.
Find the values of x and y
(i)
x
=
38.59°
,
y
=
38.59°
(ii)
x
=
39.59°
,
y
=
39.59°
(iii)
x
=
42.59°
,
y
=
42.59°
(iv)
x
=
41.59°
,
y
=
41.59°
(v)
x
=
40.59°
,
y
=
40.59°
Question
23
23.
In the figure given below,
HIJK
is a rhombus.
Find the values of x and y
(i)
x
=
58.95°
,
y
=
58.95°
(ii)
x
=
59.95°
,
y
=
59.95°
(iii)
x
=
55.95°
,
y
=
55.95°
(iv)
x
=
57.95°
,
y
=
57.95°
(v)
x
=
56.95°
,
y
=
56.95°
Question
24
24.
In the figure given below,
OPQR
is a rhombus.
Find the values of x and y
(i)
x
=
25.48°
,
y
=
68.52°
(ii)
x
=
22.48°
,
y
=
65.52°
(iii)
x
=
24.48°
,
y
=
67.52°
(iv)
x
=
23.48°
,
y
=
66.52°
(v)
x
=
21.48°
,
y
=
64.52°
Question
25
25.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
G
=
62°
,
H
=
119°
,
I
=
58°
,
J
=
121°
(ii)
G
=
61°
,
H
=
119°
,
I
=
62°
,
J
=
118°
(iii)
G
=
58°
,
H
=
122°
,
I
=
59°
,
J
=
121°
(iv)
G
=
59°
,
H
=
118°
,
I
=
61°
,
J
=
122°
(v)
G
=
60°
,
H
=
120°
,
I
=
60°
,
J
=
120°
Question
26
26.
In the adjoining figure,
MNOP
is a trapezium in which
MN
∥
OP
.
If
x = 56.1°
and
y = 78.25°
,
find the measures of
∠O
and
∠P
.
(i)
O
=
101.75°
,
P
=
123.9°
(ii)
O
=
100.75°
,
P
=
122.9°
(iii)
O
=
103.75°
,
P
=
125.9°
(iv)
O
=
99.75°
,
P
=
121.9°
(v)
O
=
102.75°
,
P
=
124.9°
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 = 44.1° and ∠ABO = 54.31°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 45.9° , b = 36.69° , c = 53.31° , d = 47.9° , e = 42.1°
(ii)
a = 45.9° , b = 35.69° , c = 54.31° , d = 45.9° , e = 44.1°
(iii)
a = 45.9° , b = 36.69° , c = 54.31° , d = 45.9° , e = 44.1°
(iv)
a = 45.9° , b = 36.69° , c = 53.31° , d = 47.9° , e = 44.1°
(v)
a = 45.9° , b = 36.69° , c = 53.31° , d = 45.9° , e = 44.1°
Question
28
28.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
3 : 7
,
find the angles of
△OAB
.
(i)
O
=
90°
,
A
=
27°
,
B
=
63°
(ii)
O
=
88°
,
A
=
29°
,
B
=
63°
(iii)
O
=
92°
,
A
=
27°
,
B
=
61°
(iv)
O
=
90°
,
A
=
25°
,
B
=
65°
(v)
O
=
88°
,
A
=
27°
,
B
=
65°
Question
29
29.
The measures of three angles of a quadrilateral are
54.31°
,
136.98°
and
57.2°
. Find the fourth angle
(i)
111.51°
(ii)
126.51°
(iii)
141.51°
(iv)
116.51°
(v)
121.51°
Question
30
30.
Find the missing angle in the given quadrilateral
(i)
124.33°
(ii)
129.33°
(iii)
114.33°
(iv)
119.33°
(v)
144.33°
Question
31
31.
Find the missing angle in the given trapezium
(i)
151.98°
(ii)
136.98°
(iii)
131.98°
(iv)
126.98°
(v)
121.98°
Question
32
32.
Find the missing angle in the given parallelogram
(i)
139.19°
(ii)
114.19°
(iii)
119.19°
(iv)
124.19°
(v)
109.19°
Question
33
33.
Find the missing angle in the given rhombus
(i)
78.3°
(ii)
68.3°
(iii)
73.3°
(iv)
93.3°
(v)
63.3°
Question
34
34.
In the adjoining figure,
CDEF
is a parallelogram and
GH
is such that
GH
∥
CE
If
∠CFG = 23.02°
and
∠EFH = 27.68°
,
find the measure of
∠CDE
.
(i)
131.31°
(ii)
130.31°
(iii)
128.31°
(iv)
127.31°
(v)
129.31°
Question
35
35.
In the adjoining figure, GHIJ is a square. A line segment JL cuts the side HI at L and the diagonal GI at K such that ∠JKI = 93.57° and ∠KLI = x°. Find the value of x .
(i)
47.57°
(ii)
48.57°
(iii)
49.57°
(iv)
50.57°
(v)
46.57°
Question
36
36.
In the adjoining figure, GHIJ is a rhombus and △KJI is an equilateral triangle. K and H are on opposite sides of IJ. If ∠JGH = 42.3°, find the values of x and y .
(i)
x
=
28°
,
y
=
36.85°
(ii)
x
=
30°
,
y
=
38.85°
(iii)
x
=
31°
,
y
=
39.85°
(iv)
x
=
32°
,
y
=
40.85°
(v)
x
=
29°
,
y
=
37.85°
Question
37
37.
In the adjoining figure, equilateral △DCE surmounts square ABCD. If CEB = x°, find the value of x.
(i)
14°
(ii)
15°
(iii)
16°
(iv)
17°
(v)
13°
Question
38
38.
In the given figure,
BCDE
is a rectangle whose diagonals intersect at
F
.
Diagonal
CE
is produced to
T
and
∠DCT =
156.04°
. Find the angles of
△FDE
.
(i)
F
=
45.92°
,
D
=
66.04°
,
E
=
68.04°
(ii)
F
=
47.92°
,
D
=
64.04°
,
E
=
68.04°
(iii)
F
=
45.92°
,
D
=
68.04°
,
E
=
66.04°
(iv)
F
=
47.92°
,
D
=
66.04°
,
E
=
66.04°
(v)
F
=
49.92°
,
D
=
66.04°
,
E
=
64.04°
Question
39
39.
In the given figure,
EFGH
is a kite whose diagonals intersect at
I
.
If
∠FGH = 43.16°
and
∠GHE = 138°
, calculate
∠IEF
and
∠GIF
.
(i)
x
=
19.42°
,
y
=
89°
(ii)
x
=
22.42°
,
y
=
92°
(iii)
x
=
20.42°
,
y
=
90°
(iv)
x
=
18.42°
,
y
=
88°
(v)
x
=
21.42°
,
y
=
91°
Question
40
40.
△QNO
is an equilateral triangle in a square
MNOP
.
If
MO
and
QN
intersect at
R
,
then find the value of x.
(i)
77°
(ii)
74°
(iii)
76°
(iv)
75°
(v)
73°
Question
41
41.
In the adjoining figure,
H
is a point in the interior of
∠JFK
.
If
HG
⟂
FJ
and
HI
⟂
FK
and
∠JFK = 57°
,
find the measure of x .
(i)
239°
(ii)
235°
(iii)
238°
(iv)
237°
(v)
236°
Question
42
42.
In the given figure, EFGH is a parallelogram. V is the mid-point of GH.
FV
bisects
∠F
. If x =
52°
, find angle 'y'.
(i)
38°
(ii)
37°
(iii)
40°
(iv)
36°
(v)
39°
Question
43
43.
In the given figure, HIJK is a rhombus. Given x = 58°, find the value of 'y'.
(i)
34°
(ii)
31°
(iii)
32°
(iv)
33°
(v)
30°
Question
44
44.
In the given figure, CDEF is a parallelogram. DF is the diagonal
such that
CF = DF = DE
. Given
∠C = 52°
, find
∠FDE
(i)
77°
(ii)
75°
(iii)
76°
(iv)
74°
(v)
78°
Question
45
45.
In the given figure, BCDE is a parallelogram. BN and DO are perpendicular to the diagonal CE. Given ∠ODE = 38°, find ∠ECB
(i)
52°
(ii)
50°
(iii)
54°
(iv)
53°
(v)
51°
Question
46
46.
In the given figure, DEFG is a rhombus such that ∠E = 120°. Then △DEG is
(i)
Obtuse angled triangle
(ii)
Right angled triangle
(iii)
Isosceles triangle
(iv)
Equilateral triangle
Question
47
47.
In the given figure, GHIJ is a parallelogram such that P is the mid-point of GH and GH = 2JG. Find ∠JPI
(i)
91°
(ii)
92°
(iii)
89°
(iv)
90°
(v)
88°
Assignment Key
1) (i)
2) (v)
3) (ii)
4) (i)
5) (i)
6) (iii)
7) (iii)
8) (iii)
9) (v)
10) (iv)
11) (iii)
12) (ii)
13) (iv)
14) (i)
15) (iii)
16) (ii)
17) (iii)
18) (i)
19) (i)
20) (iii)
21) (iv)
22) (v)
23) (iv)
24) (iv)
25) (v)
26) (i)
27) (ii)
28) (i)
29) (i)
30) (iii)
31) (v)
32) (v)
33) (v)
34) (v)
35) (ii)
36) (ii)
37) (ii)
38) (iv)
39) (iii)
40) (iv)
41) (iv)
42) (i)
43) (iii)
44) (iii)
45) (i)
46) (iv)
47) (iv)
