EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In parallelogram ABCD, if ∠A = 76.87°, then find the value of ∠D
(i)
104.13°
(ii)
103.13°
(iii)
101.13°
(iv)
105.13°
(v)
102.13°
Question
2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
91°
(ii)
92°
(iii)
88°
(iv)
89°
(v)
90°
Question
3
3.
The sum of the interior angles of a quadrilateral is
(i)
360°
(ii)
90°
(iii)
270°
(iv)
180°
Question
4
4.
The angles of a quadrilateral LMNO are in the ratio 10 : 19 : 18 : 25. Find the measure of each angle of the quadrilateral.
(i)
L
=
51°
,
M
=
94°
,
N
=
92°
,
O
=
123°
(ii)
L
=
50°
,
M
=
95°
,
N
=
90°
,
O
=
125°
(iii)
L
=
49°
,
M
=
93°
,
N
=
91°
,
O
=
127°
(iv)
L
=
48°
,
M
=
97°
,
N
=
89°
,
O
=
126°
(v)
L
=
52°
,
M
=
94°
,
N
=
88°
,
O
=
126°
Question
5
5.
Two adjacent angles of a parallelogram OPQR are in the ratio 9 : 9. Find the measure of each of its angles.
(i)
O
=
88°
,
P
=
92°
,
Q
=
89°
,
R
=
91°
(ii)
O
=
90°
,
P
=
90°
,
Q
=
90°
,
R
=
90°
(iii)
O
=
92°
,
P
=
89°
,
Q
=
88°
,
R
=
91°
(iv)
O
=
91°
,
P
=
89°
,
Q
=
92°
,
R
=
88°
(v)
O
=
89°
,
P
=
88°
,
Q
=
91°
,
R
=
92°
Question
6
6.
In the adjoining figure,
NOPQ
is a parallelogram in which
∠QNP = 70.92°
,
∠PNO = 58.82°
,
∠QRP = 96.38°
. Calculate
∠NOQ
(i)
23.80°
(ii)
25.80°
(iii)
26.80°
(iv)
22.80°
(v)
24.80°
Question
7
7.
In the adjoining figure,
IJKL
is a parallelogram in which
∠LIK = 55.84°
,
∠KIJ = 64.8°
,
∠LMK = 84.22°
. Calculate
∠KLJ
(i)
28.98°
(ii)
30.98°
(iii)
31.98°
(iv)
32.98°
(v)
29.98°
Question
8
8.
In the adjoining figure,
KLMN
is a parallelogram in which
∠NKM = 34.45°
,
∠MKL = 37.36°
,
∠NOM = 85.12°
. Calculate
∠LMK
(i)
33.45°
(ii)
34.45°
(iii)
36.45°
(iv)
32.45°
(v)
35.45°
Question
9
9.
In the adjoining figure,
OPQR
is a parallelogram in which
∠ROQ = 27.16°
,
∠QOP = 34.2°
,
∠RSQ = 75.79°
. Calculate
∠RPQ
(i)
48.63°
(ii)
46.63°
(iii)
50.63°
(iv)
47.63°
(v)
49.63°
Question
10
10.
In the adjoining figure,
MNOP
is a rectangle.
If
∠OMN = 41.63°
, find
∠NOM
(i)
50.37°
(ii)
46.37°
(iii)
47.37°
(iv)
49.37°
(v)
48.37°
Question
11
11.
Three angles of quadrilateral measure 89.23°, 76.87° and 44.42° respectively. Find the measure of the fourth angle
(i)
150.48°
(ii)
149.48°
(iii)
148.48°
(iv)
147.48°
(v)
151.48°
Question
12
12.
Three angles of a quadrilateral are equal and the fourth angle measure 86.42°. What is the measure of each of the equal angles?
(i)
92.19°
(ii)
93.19°
(iii)
90.19°
(iv)
91.19°
(v)
89.19°
Question
13
13.
Two angles of a quadrilateral are of measure 66.03° and 61.58° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
117.19°
(ii)
116.19°
(iii)
115.19°
(iv)
114.19°
(v)
118.19°
Question
14
14.
A quadrilateral has three acute angles, each measuring 43°. What is the measure of its fourth angle?
(i)
230.00°
(ii)
229.00°
(iii)
233.00°
(iv)
232.00°
(v)
231.00°
Question
15
15.
One angle of a parallelogram measures
H
=
55.83°
.
Find the measure of each of its remaining angles.
(i)
I
=
125.17°
,
J
=
56.83°
,
K
=
125.17°
(ii)
I
=
122.17°
,
J
=
53.83°
,
K
=
122.17°
(iii)
I
=
126.17°
,
J
=
57.83°
,
K
=
126.17°
(iv)
I
=
123.17°
,
J
=
54.83°
,
K
=
123.17°
(v)
I
=
124.17°
,
J
=
55.83°
,
K
=
124.17°
Question
16
16.
Two adjacent angles of a parallelogram are in the ratio
6 : 30
.
Find the measure of each of its angles.
(i)
A
=
30°
,
B
=
150°
,
C
=
30°
,
D
=
150°
(ii)
A
=
29°
,
B
=
148°
,
C
=
31°
,
D
=
152°
(iii)
A
=
28°
,
B
=
152°
,
C
=
29°
,
D
=
151°
(iv)
A
=
32°
,
B
=
149°
,
C
=
28°
,
D
=
151°
(v)
A
=
31°
,
B
=
149°
,
C
=
32°
,
D
=
148°
Question
17
17.
In the figure given below,
MNOP
is a rectangle.
Find the values of x and y
(i)
x
=
37.25°
,
y
=
73.5°
(ii)
x
=
36.25°
,
y
=
72.5°
(iii)
x
=
34.25°
,
y
=
70.5°
(iv)
x
=
35.25°
,
y
=
71.5°
(v)
x
=
38.25°
,
y
=
74.5°
Question
18
18.
In the figure given below,
CDEF
is a rectangle.
Find the values of x and y
(i)
x
=
43.88°
,
y
=
48.12°
(ii)
x
=
41.88°
,
y
=
46.12°
(iii)
x
=
42.88°
,
y
=
47.12°
(iv)
x
=
40.88°
,
y
=
45.12°
(v)
x
=
44.88°
,
y
=
49.12°
Question
19
19.
In the figure given below,
ABCD
is a rhombus.
Find the values of x and y
(i)
x
=
41.74°
,
y
=
41.74°
(ii)
x
=
43.74°
,
y
=
43.74°
(iii)
x
=
42.74°
,
y
=
42.74°
(iv)
x
=
39.74°
,
y
=
39.74°
(v)
x
=
40.74°
,
y
=
40.74°
Question
20
20.
In the figure given below,
GHIJ
is a rhombus.
Find the values of x and y
(i)
x
=
64.42°
,
y
=
64.42°
(ii)
x
=
68.42°
,
y
=
68.42°
(iii)
x
=
65.42°
,
y
=
65.42°
(iv)
x
=
66.42°
,
y
=
66.42°
(v)
x
=
67.42°
,
y
=
67.42°
Question
21
21.
In the figure given below,
FGHI
is a rhombus.
Find the values of x and y
(i)
x
=
21.59°
,
y
=
72.41°
(ii)
x
=
20.59°
,
y
=
71.41°
(iii)
x
=
18.59°
,
y
=
69.41°
(iv)
x
=
19.59°
,
y
=
70.41°
(v)
x
=
17.59°
,
y
=
68.41°
Question
22
22.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
N
=
59°
,
O
=
118°
,
P
=
61°
,
Q
=
122°
(ii)
N
=
62°
,
O
=
119°
,
P
=
58°
,
Q
=
121°
(iii)
N
=
58°
,
O
=
122°
,
P
=
59°
,
Q
=
121°
(iv)
N
=
61°
,
O
=
119°
,
P
=
62°
,
Q
=
118°
(v)
N
=
60°
,
O
=
120°
,
P
=
60°
,
Q
=
120°
Question
23
23.
In the adjoining figure,
LMNO
is a trapezium in which
LM
∥
NO
.
If
x = 98.91°
and
y = 122.11°
,
find the measures of
∠L
and
∠M
.
(i)
L
=
57.89°
,
M
=
81.09°
(ii)
L
=
58.89°
,
M
=
82.09°
(iii)
L
=
56.89°
,
M
=
80.09°
(iv)
L
=
59.89°
,
M
=
83.09°
(v)
L
=
55.89°
,
M
=
79.09°
Question
24
24.
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 = 28.36° and ∠ABO = 59.61°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 61.64° , b = 31.39° , c = 58.61° , d = 61.64° , e = 28.36°
(ii)
a = 61.64° , b = 31.39° , c = 58.61° , d = 63.64° , e = 26.36°
(iii)
a = 61.64° , b = 30.39° , c = 59.61° , d = 61.64° , e = 28.36°
(iv)
a = 61.64° , b = 31.39° , c = 59.61° , d = 61.64° , e = 28.36°
(v)
a = 61.64° , b = 31.39° , c = 58.61° , d = 63.64° , e = 28.36°
Question
25
25.
In the adjoining figure, side FG of parallelogram EFGH has been produced to I. If ∠HGI = 94.76° , find the measure of each angle of the parallelogram.
(i)
E
=
86.24°
,
F
=
93.76°
,
G
=
87.24°
,
H
=
92.76°
(ii)
E
=
84.24°
,
F
=
92.76°
,
G
=
86.24°
,
H
=
96.76°
(iii)
E
=
83.24°
,
F
=
96.76°
,
G
=
84.24°
,
H
=
95.76°
(iv)
E
=
87.24°
,
F
=
93.76°
,
G
=
83.24°
,
H
=
95.76°
(v)
E
=
85.24°
,
F
=
94.76°
,
G
=
85.24°
,
H
=
94.76°
Question
26
26.
In the adjoining figure,
EFGH
is a parallelogram and
IJ
is such that
IJ
∥
EG
If
∠EHI = 31.41°
and
∠GHJ = 25.9°
,
find the measure of
∠EFG
.
(i)
124.69°
(ii)
123.69°
(iii)
120.69°
(iv)
121.69°
(v)
122.69°
Question
27
27.
In the adjoining figure, FGHI is a square. A line segment IK cuts the side GH at K and the diagonal FH at J such that ∠IJH = 105.86° and ∠JKH = x°. Find the value of x .
(i)
58.86°
(ii)
62.86°
(iii)
59.86°
(iv)
61.86°
(v)
60.86°
Question
28
28.
In the adjoining figure, MNOP is a rhombus and △QPO is an equilateral triangle. Q and N are on opposite sides of OP. If ∠PMN = 87.8°, find the values of x and y .
(i)
x
=
30°
,
y
=
16.1°
(ii)
x
=
28°
,
y
=
14.1°
(iii)
x
=
31°
,
y
=
17.1°
(iv)
x
=
32°
,
y
=
18.1°
(v)
x
=
29°
,
y
=
15.1°
Question
29
29.
In the adjoining figure, equilateral △LKM surmounts square IJKL. If KMJ = x°, find the value of x.
(i)
14°
(ii)
13°
(iii)
15°
(iv)
17°
(v)
16°
Question
30
30.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
6 : 12
,
find the angles of
△OAB
.
(i)
O
=
88°
,
A
=
32°
,
B
=
60°
(ii)
O
=
90°
,
A
=
30°
,
B
=
60°
(iii)
O
=
90°
,
A
=
28°
,
B
=
62°
(iv)
O
=
92°
,
A
=
30°
,
B
=
58°
(v)
O
=
88°
,
A
=
30°
,
B
=
62°
Question
31
31.
In the given figure,
CDEF
is a rectangle whose diagonals intersect at
G
.
Diagonal
CE
is produced to
T
and
∠FET =
127.88°
. Find the angles of
△GFC
.
(i)
G
=
102.24°
,
F
=
37.88°
,
C
=
39.88°
(ii)
G
=
102.24°
,
F
=
39.88°
,
C
=
37.88°
(iii)
G
=
104.24°
,
F
=
37.88°
,
C
=
37.88°
(iv)
G
=
104.24°
,
F
=
35.88°
,
C
=
39.88°
(v)
G
=
106.24°
,
F
=
37.88°
,
C
=
35.88°
Question
32
32.
In the given figure,
IJKL
is a kite whose diagonals intersect at
M
.
If
∠LIJ = 61.11°
and
∠IJK = 98.92°
, calculate
∠MLI
and
∠MKL
.
(i)
x
=
58.44°
,
y
=
49.53°
(ii)
x
=
59.44°
,
y
=
50.53°
(iii)
x
=
61.44°
,
y
=
52.53°
(iv)
x
=
57.44°
,
y
=
48.53°
(v)
x
=
60.44°
,
y
=
51.53°
Question
33
33.
△MLI
is an equilateral triangle in a square
IJKL
.
If
IK
and
ML
intersect at
N
,
then find the value of x.
(i)
74°
(ii)
76°
(iii)
75°
(iv)
77°
(v)
73°
Question
34
34.
In the adjoining figure,
G
is a point in the interior of
∠IEJ
.
If
GF
⟂
EI
and
GH
⟂
EJ
and
∠IEJ = 47°
,
find the measure of x .
(i)
225°
(ii)
226°
(iii)
227°
(iv)
229°
(v)
228°
Question
35
35.
Find the missing angle in the given quadrilateral
(i)
62.41°
(ii)
82.41°
(iii)
67.41°
(iv)
57.41°
(v)
52.41°
Question
36
36.
Find the missing angle in the given trapezium
(i)
128.04°
(ii)
98.04°
(iii)
103.04°
(iv)
113.04°
(v)
108.04°
Question
37
37.
Find the missing angle in the given parallelogram
(i)
82.19°
(ii)
67.19°
(iii)
52.19°
(iv)
57.19°
(v)
62.19°
Question
38
38.
Find the missing angle in the given rhombus
(i)
94°
(ii)
69°
(iii)
64°
(iv)
74°
(v)
79°
Question
39
39.
In the given figure, FGHI is a parallelogram.
If
FV
and
GV
are bisector of
∠F
&
∠G
, find
∠V
(i)
88°
(ii)
91°
(iii)
90°
(iv)
89°
(v)
92°
Question
40
40.
In the given figure, CDEF is a parallelogram. V is the mid-point of EF.
DV
bisects
∠D
. If x =
52°
, find angle 'y'.
(i)
38°
(ii)
39°
(iii)
37°
(iv)
36°
(v)
40°
Question
41
41.
In the given figure, DEFG is a quadrilateral. QG and QF are bisectors of ∠G & ∠F meeting at Q. Find ∠FQG
(i)
95.0°
(ii)
94.0°
(iii)
96.0°
(iv)
93.0°
(v)
97.0°
Question
42
42.
In the given figure, EFGH is a rhombus. Given x = 56°, find the value of 'y'.
(i)
34°
(ii)
35°
(iii)
32°
(iv)
33°
(v)
36°
Question
43
43.
In the given figure, GHIJ is a parallelogram. GI bisects ∠G & ∠I.
Given
GI = 12 cm
and
HJ = 8 cm
, find
GH
(i)
9.21 cm
(ii)
5.21 cm
(iii)
7.21 cm
(iv)
8.21 cm
(v)
6.21 cm
Question
44
44.
In the given figure, BCDE is a parallelogram. CE is the diagonal
such that
BE = CE = CD
. Given
∠B = 45°
, find
∠ECD
(i)
89°
(ii)
90°
(iii)
88°
(iv)
92°
(v)
91°
Question
45
45.
In the given figure, BCDE is a parallelogram. BP and DQ are perpendicular to the diagonal CE. Given ∠QDE = 30°, find ∠ECB
(i)
60°
(ii)
61°
(iii)
62°
(iv)
59°
(v)
58°
Question
46
46.
In the given figure, EFGH is a rhombus such that ∠F = 120°. Then △EFH is
(i)
Right angled triangle
(ii)
Obtuse angled triangle
(iii)
Equilateral triangle
(iv)
Isosceles triangle
Question
47
47.
M, N, O are the mid-points of the sides of triangle GHI.
If the perimeter of the
△GHI
is
48 cm
, the perimeter of
△MNO
is
(i)
25.0 cm
(ii)
24.0 cm
(iii)
23.0 cm
(iv)
22.0 cm
(v)
26.0 cm
Question
48
48.
CDEF is a rhombus. M, N, O and P are mid-points of sides CD, DE, EF and FC. Find ∠NOP
(i)
91°
(ii)
88°
(iii)
92°
(iv)
90°
(v)
89°
Question
49
49.
In the given figure, BCDE is a parallelogram
such that
F
and
G
are mid-points of sides
BC
&
DE
.
BG
meets
CE
at
Q
and
DF
meets
CE
at
R
. Given
CE
=
15 cm
, find
CR
(i)
6.00 cm
(ii)
3.00 cm
(iii)
4.00 cm
(iv)
5.00 cm
(v)
7.00 cm
Question
50
50.
In the given figure, DEFG is a parallelogram such that Q is the mid-point of DE and DE = 2GD. Find ∠GQF
(i)
92°
(ii)
89°
(iii)
91°
(iv)
88°
(v)
90°
Question
51
51.
BCDE is an isosceles trapezium. BR and CR are angular bisector of ∠B & ∠C. If ∠B = 66°, find ∠BRC
(i)
114°
(ii)
116°
(iii)
115°
(iv)
113°
(v)
112°
Question
52
52.
In the given figure, EFGH is a parallelogram. The bisector of the angles E, F, G & H intersect at R, S, T & U to form a quadrilateral. Find ∠RST
(i)
90°
(ii)
88°
(iii)
91°
(iv)
89°
(v)
92°
Assignment Key
1) (ii)
2) (v)
3) (i)
4) (ii)
5) (ii)
6) (v)
7) (ii)
8) (ii)
9) (i)
10) (v)
11) (ii)
12) (iv)
13) (ii)
14) (v)
15) (v)
16) (i)
17) (ii)
18) (iii)
19) (i)
20) (iv)
21) (iv)
22) (v)
23) (i)
24) (iii)
25) (v)
26) (v)
27) (v)
28) (i)
29) (iii)
30) (ii)
31) (iii)
32) (ii)
33) (iii)
34) (iii)
35) (v)
36) (ii)
37) (iii)
38) (iii)
39) (iii)
40) (i)
41) (i)
42) (i)
43) (iii)
44) (ii)
45) (i)
46) (iii)
47) (ii)
48) (iv)
49) (iv)
50) (v)
51) (i)
52) (i)
