EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In parallelogram ABCD, if ∠B = 137.71°, then find the value of ∠C
(i)
40.29°
(ii)
41.29°
(iii)
44.29°
(iv)
43.29°
(v)
42.29°
Question
2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
92°
(ii)
88°
(iii)
91°
(iv)
89°
(v)
90°
Question
3
3.
The sum of the interior angles of a quadrilateral is
(i)
180°
(ii)
270°
(iii)
90°
(iv)
360°
Question
4
4.
The angles of a quadrilateral EFGH are in the ratio 25 : 13 : 37 : 45. Find the measure of each angle of the quadrilateral.
(i)
E
=
74°
,
F
=
37°
,
G
=
112°
,
H
=
137°
(ii)
E
=
75°
,
F
=
39°
,
G
=
111°
,
H
=
135°
(iii)
E
=
73°
,
F
=
41°
,
G
=
110°
,
H
=
136°
(iv)
E
=
77°
,
F
=
38°
,
G
=
109°
,
H
=
136°
(v)
E
=
76°
,
F
=
38°
,
G
=
113°
,
H
=
133°
Question
5
5.
Two adjacent angles of a parallelogram GHIJ are in the ratio 6 : 14. Find the measure of each of its angles.
(i)
G
=
54°
,
H
=
126°
,
I
=
54°
,
J
=
126°
(ii)
G
=
56°
,
H
=
125°
,
I
=
52°
,
J
=
127°
(iii)
G
=
53°
,
H
=
124°
,
I
=
55°
,
J
=
128°
(iv)
G
=
55°
,
H
=
125°
,
I
=
56°
,
J
=
124°
(v)
G
=
52°
,
H
=
128°
,
I
=
53°
,
J
=
127°
Question
6
6.
In the adjoining figure,
LMNO
is a parallelogram in which
∠OLN = 18.67°
,
∠NLM = 21.09°
,
∠OPN = 77.98°
. Calculate
∠LMO
(i)
82.93°
(ii)
80.93°
(iii)
78.93°
(iv)
81.93°
(v)
79.93°
Question
7
7.
In the adjoining figure,
GHIJ
is a parallelogram in which
∠JGI = 9.18°
,
∠IGH = 17.79°
,
∠JKI = 33.19°
. Calculate
∠IJH
(i)
130.02°
(ii)
131.02°
(iii)
129.02°
(iv)
127.02°
(v)
128.02°
Question
8
8.
In the adjoining figure,
PQRS
is a parallelogram in which
∠SPR = 21.77°
,
∠RPQ = 22.8°
,
∠STR = 85.2°
. Calculate
∠QRP
(i)
23.77°
(ii)
20.77°
(iii)
22.77°
(iv)
19.77°
(v)
21.77°
Question
9
9.
In the adjoining figure,
DEFG
is a parallelogram in which
∠GDF = 39.76°
,
∠FDE = 43.96°
,
∠GHF = 84.18°
. Calculate
∠GEF
(i)
46.42°
(ii)
45.42°
(iii)
43.42°
(iv)
44.42°
(v)
42.42°
Question
10
10.
In the adjoining figure,
HIJK
is a rectangle.
If
∠JHI = 43.36°
, find
∠HIK
(i)
42.36°
(ii)
45.36°
(iii)
44.36°
(iv)
43.36°
(v)
41.36°
Question
11
11.
Three angles of quadrilateral measure 62.48°, 69.09° and 92.48° respectively. Find the measure of the fourth angle
(i)
135.95°
(ii)
134.95°
(iii)
133.95°
(iv)
136.95°
(v)
137.95°
Question
12
12.
Three angles of a quadrilateral are equal and the fourth angle measure 139.28°. What is the measure of each of the equal angles?
(i)
71.57°
(ii)
75.57°
(iii)
73.57°
(iv)
74.57°
(v)
72.57°
Question
13
13.
Two angles of a quadrilateral are of measure 55.15° and 124.85° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
89.00°
(ii)
91.00°
(iii)
88.00°
(iv)
90.00°
(v)
92.00°
Question
14
14.
A quadrilateral has three acute angles, each measuring 72°. What is the measure of its fourth angle?
(i)
143.00°
(ii)
144.00°
(iii)
145.00°
(iv)
146.00°
(v)
142.00°
Question
15
15.
One angle of a parallelogram measures
I
=
50.13°
.
Find the measure of each of its remaining angles.
(i)
J
=
128.87°
,
K
=
49.13°
,
L
=
128.87°
(ii)
J
=
130.87°
,
K
=
51.13°
,
L
=
130.87°
(iii)
J
=
131.87°
,
K
=
52.13°
,
L
=
131.87°
(iv)
J
=
127.87°
,
K
=
48.13°
,
L
=
127.87°
(v)
J
=
129.87°
,
K
=
50.13°
,
L
=
129.87°
Question
16
16.
Two adjacent angles of a parallelogram are in the ratio
38 : 52
.
Find the measure of each of its angles.
(i)
A
=
75°
,
B
=
102°
,
C
=
77°
,
D
=
106°
(ii)
A
=
78°
,
B
=
103°
,
C
=
74°
,
D
=
105°
(iii)
A
=
76°
,
B
=
104°
,
C
=
76°
,
D
=
104°
(iv)
A
=
77°
,
B
=
103°
,
C
=
78°
,
D
=
102°
(v)
A
=
74°
,
B
=
106°
,
C
=
75°
,
D
=
105°
Question
17
17.
In the figure given below,
JKLM
is a rectangle.
Find the values of x and y
(i)
x
=
51.2°
,
y
=
101.4°
(ii)
x
=
48.2°
,
y
=
98.4°
(iii)
x
=
50.2°
,
y
=
100.4°
(iv)
x
=
49.2°
,
y
=
99.4°
(v)
x
=
52.2°
,
y
=
102.4°
Question
18
18.
In the figure given below,
GHIJ
is a rectangle.
Find the values of x and y
(i)
x
=
27.76°
,
y
=
62.24°
(ii)
x
=
29.76°
,
y
=
64.24°
(iii)
x
=
28.76°
,
y
=
63.24°
(iv)
x
=
26.76°
,
y
=
61.24°
(v)
x
=
25.76°
,
y
=
60.24°
Question
19
19.
In the figure given below,
BCDE
is a rhombus.
Find the values of x and y
(i)
x
=
34.29°
,
y
=
34.29°
(ii)
x
=
33.29°
,
y
=
33.29°
(iii)
x
=
35.29°
,
y
=
35.29°
(iv)
x
=
37.29°
,
y
=
37.29°
(v)
x
=
36.29°
,
y
=
36.29°
Question
20
20.
In the figure given below,
HIJK
is a rhombus.
Find the values of x and y
(i)
x
=
54.71°
,
y
=
54.71°
(ii)
x
=
51.71°
,
y
=
51.71°
(iii)
x
=
52.71°
,
y
=
52.71°
(iv)
x
=
53.71°
,
y
=
53.71°
(v)
x
=
55.71°
,
y
=
55.71°
Question
21
21.
In the figure given below,
KLMN
is a rhombus.
Find the values of x and y
(i)
x
=
38.29°
,
y
=
53.71°
(ii)
x
=
35.29°
,
y
=
50.71°
(iii)
x
=
39.29°
,
y
=
54.71°
(iv)
x
=
36.29°
,
y
=
51.71°
(v)
x
=
37.29°
,
y
=
52.71°
Question
22
22.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
C
=
61°
,
D
=
119°
,
E
=
62°
,
F
=
118°
(ii)
C
=
59°
,
D
=
118°
,
E
=
61°
,
F
=
122°
(iii)
C
=
62°
,
D
=
119°
,
E
=
58°
,
F
=
121°
(iv)
C
=
60°
,
D
=
120°
,
E
=
60°
,
F
=
120°
(v)
C
=
58°
,
D
=
122°
,
E
=
59°
,
F
=
121°
Question
23
23.
In the adjoining figure,
JKLM
is a trapezium in which
JK
∥
LM
.
If
x = 53.13°
and
y = 68.88°
,
find the measures of
∠L
and
∠M
.
(i)
L
=
113.12°
,
M
=
128.87°
(ii)
L
=
109.12°
,
M
=
124.87°
(iii)
L
=
110.12°
,
M
=
125.87°
(iv)
L
=
111.12°
,
M
=
126.87°
(v)
L
=
112.12°
,
M
=
127.87°
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 = 36.13° and ∠ABO = 59.53°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 53.87° , b = 31.47° , c = 58.53° , d = 53.87° , e = 36.13°
(ii)
a = 53.87° , b = 31.47° , c = 59.53° , d = 53.87° , e = 36.13°
(iii)
a = 53.87° , b = 31.47° , c = 58.53° , d = 55.87° , e = 34.13°
(iv)
a = 53.87° , b = 30.47° , c = 59.53° , d = 53.87° , e = 36.13°
(v)
a = 53.87° , b = 31.47° , c = 58.53° , d = 55.87° , e = 36.13°
Question
25
25.
In the adjoining figure, side OP of parallelogram MNOP has been produced to Q. If ∠NOQ = 111.16° , find the measure of each angle of the parallelogram.
(i)
M
=
70.84°
,
N
=
110.16°
,
O
=
66.84°
,
P
=
112.16°
(ii)
M
=
67.84°
,
N
=
109.16°
,
O
=
69.84°
,
P
=
113.16°
(iii)
M
=
66.84°
,
N
=
113.16°
,
O
=
67.84°
,
P
=
112.16°
(iv)
M
=
69.84°
,
N
=
110.16°
,
O
=
70.84°
,
P
=
109.16°
(v)
M
=
68.84°
,
N
=
111.16°
,
O
=
68.84°
,
P
=
111.16°
Question
26
26.
In the adjoining figure,
LMNO
is a parallelogram and
PQ
is such that
PQ
∥
LN
If
∠LOP = 29.63°
and
∠NOQ = 22.18°
,
find the measure of
∠LMN
.
(i)
129.19°
(ii)
126.19°
(iii)
128.19°
(iv)
130.19°
(v)
127.19°
Question
27
27.
In the adjoining figure, BCDE is a square. A line segment EG cuts the side CD at G and the diagonal BD at F such that ∠EFD = 106.22° and ∠FGD = x°. Find the value of x .
(i)
62.22°
(ii)
59.22°
(iii)
60.22°
(iv)
63.22°
(v)
61.22°
Question
28
28.
In the adjoining figure, EFGH is a rhombus and △IHG is an equilateral triangle. I and F are on opposite sides of GH. If ∠HEF = 87.8°, find the values of x and y .
(i)
x
=
31°
,
y
=
17.1°
(ii)
x
=
28°
,
y
=
14.1°
(iii)
x
=
29°
,
y
=
15.1°
(iv)
x
=
30°
,
y
=
16.1°
(v)
x
=
32°
,
y
=
18.1°
Question
29
29.
In the adjoining figure, equilateral △QPR surmounts square NOPQ. If PRN = x°, find the value of x.
(i)
44°
(ii)
45°
(iii)
46°
(iv)
47°
(v)
43°
Question
30
30.
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
=
90°
,
A
=
45°
,
B
=
45°
(iii)
O
=
90°
,
A
=
43°
,
B
=
47°
(iv)
O
=
88°
,
A
=
45°
,
B
=
47°
(v)
O
=
88°
,
A
=
47°
,
B
=
45°
Question
31
31.
In the given figure,
KLMN
is a rectangle whose diagonals intersect at
O
.
Diagonal
LN
is produced to
T
and
∠KNT =
129.29°
. Find the angles of
△OKL
.
(i)
O
=
99.42°
,
K
=
41.29°
,
L
=
39.29°
(ii)
O
=
101.42°
,
K
=
37.29°
,
L
=
41.29°
(iii)
O
=
103.42°
,
K
=
39.29°
,
L
=
37.29°
(iv)
O
=
101.42°
,
K
=
39.29°
,
L
=
39.29°
(v)
O
=
99.42°
,
K
=
39.29°
,
L
=
41.29°
Question
32
32.
In the given figure,
KLMN
is a kite whose diagonals intersect at
O
.
If
∠NKL = 94.46°
and
∠KLM = 100.56°
, calculate
∠ONK
and
∠OMN
.
(i)
x
=
42.77°
,
y
=
32.21°
(ii)
x
=
40.77°
,
y
=
30.21°
(iii)
x
=
44.77°
,
y
=
34.21°
(iv)
x
=
41.77°
,
y
=
31.21°
(v)
x
=
43.77°
,
y
=
33.21°
Question
33
33.
△NMJ
is an equilateral triangle in a square
JKLM
.
If
KM
and
JN
intersect at
O
,
then find the value of x.
(i)
77°
(ii)
74°
(iii)
75°
(iv)
76°
(v)
73°
Question
34
34.
In the adjoining figure,
P
is a point in the interior of
∠RNS
.
If
PO
⟂
NR
and
PQ
⟂
NS
and
∠RNS = 32°
,
find the measure of x .
(i)
210°
(ii)
214°
(iii)
213°
(iv)
212°
(v)
211°
Question
35
35.
Find the missing angle in the given quadrilateral
(i)
132.88°
(ii)
142.88°
(iii)
137.88°
(iv)
157.88°
(v)
127.88°
Question
36
36.
Find the missing angle in the given trapezium
(i)
104.22°
(ii)
99.22°
(iii)
109.22°
(iv)
129.22°
(v)
114.22°
Question
37
37.
Find the missing angle in the given parallelogram
(i)
80.18°
(ii)
70.18°
(iii)
65.18°
(iv)
95.18°
(v)
75.18°
Question
38
38.
Find the missing angle in the given rhombus
(i)
92.43°
(ii)
87.43°
(iii)
82.43°
(iv)
107.43°
(v)
77.43°
Question
39
39.
In the given figure, CDEF is a parallelogram.
If
CU
and
DU
are bisector of
∠C
&
∠D
, find
∠U
(i)
91°
(ii)
92°
(iii)
90°
(iv)
89°
(v)
88°
Question
40
40.
In the given figure, HIJK is a parallelogram. R is the mid-point of JK.
IR
bisects
∠I
. If x =
52°
, find angle 'y'.
(i)
39°
(ii)
38°
(iii)
40°
(iv)
36°
(v)
37°
Question
41
41.
In the given figure, GHIJ is a quadrilateral. RJ and RI are bisectors of ∠J & ∠I meeting at R. Find ∠IRJ
(i)
84.0°
(ii)
86.0°
(iii)
85.0°
(iv)
82.0°
(v)
83.0°
Question
42
42.
In the given figure, EFGH is a rhombus. Given x = 67°, find the value of 'y'.
(i)
25°
(ii)
22°
(iii)
21°
(iv)
23°
(v)
24°
Question
43
43.
In the given figure, BCDE is a parallelogram. BD bisects ∠B & ∠D.
Given
BD = 9 cm
and
CE = 6 cm
, find
BC
(i)
3.41 cm
(ii)
6.41 cm
(iii)
4.41 cm
(iv)
7.41 cm
(v)
5.41 cm
Question
44
44.
In the given figure, FGHI is a parallelogram. GI is the diagonal
such that
FI = GI = GH
. Given
∠F = 61°
, find
∠IGH
(i)
60°
(ii)
57°
(iii)
59°
(iv)
58°
(v)
56°
Question
45
45.
In the given figure, GHIJ is a parallelogram. GN and IO are perpendicular to the diagonal HJ. Given ∠OIJ = 31°, find ∠JHG
(i)
60°
(ii)
58°
(iii)
61°
(iv)
59°
(v)
57°
Question
46
46.
In the given figure, IJKL is a rhombus such that ∠J = 120°. Then △IJL is
(i)
Obtuse angled triangle
(ii)
Right angled triangle
(iii)
Equilateral triangle
(iv)
Isosceles triangle
Question
47
47.
P, Q, R are the mid-points of the sides of triangle FGH.
If the perimeter of the
△FGH
is
52 cm
, the perimeter of
△PQR
is
(i)
25.0 cm
(ii)
28.0 cm
(iii)
24.0 cm
(iv)
27.0 cm
(v)
26.0 cm
Question
48
48.
BCDE is a rhombus. M, N, O and P are mid-points of sides BC, CD, DE and EB. Find ∠NOP
(i)
92°
(ii)
89°
(iii)
88°
(iv)
91°
(v)
90°
Question
49
49.
In the given figure, DEFG is a parallelogram
such that
H
and
I
are mid-points of sides
DE
&
FG
.
DI
meets
EG
at
S
and
FH
meets
EG
at
T
. Given
EG
=
20 cm
, find
SG
(i)
7.67 cm
(ii)
8.67 cm
(iii)
4.67 cm
(iv)
6.67 cm
(v)
5.67 cm
Question
50
50.
In the given figure, EFGH is a parallelogram such that Q is the mid-point of EF and EF = 2HE. Find ∠HQG
(i)
88°
(ii)
92°
(iii)
89°
(iv)
91°
(v)
90°
Question
51
51.
ABCD is an isosceles trapezium. AQ and BQ are angular bisector of ∠A & ∠B. If ∠A = 61°, find ∠AQB
(i)
120°
(ii)
117°
(iii)
121°
(iv)
119°
(v)
118°
Question
52
52.
In the given figure, ABCD is a parallelogram. The bisector of the angles A, B, C & D intersect at Q, R, S & T to form a quadrilateral. Find ∠TQR
(i)
88°
(ii)
92°
(iii)
91°
(iv)
89°
(v)
90°
Assignment Key
1) (v)
2) (v)
3) (iv)
4) (ii)
5) (i)
6) (ii)
7) (iii)
8) (v)
9) (iv)
10) (iv)
11) (i)
12) (iii)
13) (iv)
14) (ii)
15) (v)
16) (iii)
17) (iii)
18) (i)
19) (iii)
20) (iv)
21) (v)
22) (iv)
23) (iv)
24) (iv)
25) (v)
26) (iii)
27) (v)
28) (iv)
29) (ii)
30) (ii)
31) (iv)
32) (i)
33) (iii)
34) (iv)
35) (v)
36) (ii)
37) (iii)
38) (v)
39) (iii)
40) (ii)
41) (i)
42) (iv)
43) (v)
44) (iv)
45) (iv)
46) (iii)
47) (v)
48) (v)
49) (iv)
50) (v)
51) (iv)
52) (v)
