EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In parallelogram ABCD, if ∠B = 133.05°, then find the value of ∠C
(i)
45.95°
(ii)
47.95°
(iii)
48.95°
(iv)
46.95°
(v)
44.95°
Question
2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
89°
(ii)
92°
(iii)
88°
(iv)
91°
(v)
90°
Question
3
3.
The sum of the interior angles of a quadrilateral is
(i)
360°
(ii)
270°
(iii)
90°
(iv)
180°
Question
4
4.
The angles of a quadrilateral DEFG are in the ratio 5 : 4 : 6 : 9. Find the measure of each angle of the quadrilateral.
(i)
D
=
73°
,
E
=
62°
,
F
=
89°
,
G
=
136°
(ii)
D
=
74°
,
E
=
58°
,
F
=
91°
,
G
=
137°
(iii)
D
=
75°
,
E
=
60°
,
F
=
90°
,
G
=
135°
(iv)
D
=
77°
,
E
=
59°
,
F
=
88°
,
G
=
136°
(v)
D
=
76°
,
E
=
59°
,
F
=
92°
,
G
=
133°
Question
5
5.
Two adjacent angles of a parallelogram ABCD are in the ratio 24 : 66. Find the measure of each of its angles.
(i)
A
=
50°
,
B
=
131°
,
C
=
46°
,
D
=
133°
(ii)
A
=
49°
,
B
=
131°
,
C
=
50°
,
D
=
130°
(iii)
A
=
46°
,
B
=
134°
,
C
=
47°
,
D
=
133°
(iv)
A
=
48°
,
B
=
132°
,
C
=
48°
,
D
=
132°
(v)
A
=
47°
,
B
=
130°
,
C
=
49°
,
D
=
134°
Question
6
6.
In the adjoining figure,
DEFG
is a parallelogram in which
∠GDF = 16.66°
,
∠FDE = 23.53°
,
∠GHF = 61.06°
. Calculate
∠DEG
(i)
97.41°
(ii)
96.41°
(iii)
94.41°
(iv)
95.41°
(v)
93.41°
Question
7
7.
In the adjoining figure,
FGHI
is a parallelogram in which
∠IFH = 35.08°
,
∠HFG = 27.39°
,
∠IJH = 104.19°
. Calculate
∠HIG
(i)
47.42°
(ii)
50.42°
(iii)
46.42°
(iv)
49.42°
(v)
48.42°
Question
8
8.
In the adjoining figure,
DEFG
is a parallelogram in which
∠GDF = 30.52°
,
∠FDE = 18.13°
,
∠GHF = 122.45°
. Calculate
∠EFD
(i)
30.52°
(ii)
31.52°
(iii)
29.52°
(iv)
28.52°
(v)
32.52°
Question
9
9.
In the adjoining figure,
FGHI
is a parallelogram in which
∠IFH = 11.65°
,
∠HFG = 21.95°
,
∠IJH = 38.97°
. Calculate
∠IGH
(i)
29.31°
(ii)
27.31°
(iii)
28.31°
(iv)
25.31°
(v)
26.31°
Question
10
10.
In the adjoining figure,
EFGH
is a rectangle.
If
∠GEF = 51.71°
, find
∠FGE
(i)
39.29°
(ii)
37.29°
(iii)
36.29°
(iv)
38.29°
(v)
40.29°
Question
11
11.
Three angles of quadrilateral measure 99.59°, 92.63° and 69.56° respectively. Find the measure of the fourth angle
(i)
97.22°
(ii)
99.22°
(iii)
100.22°
(iv)
96.22°
(v)
98.22°
Question
12
12.
Three angles of a quadrilateral are equal and the fourth angle measure 64.78°. What is the measure of each of the equal angles?
(i)
99.41°
(ii)
97.41°
(iii)
100.41°
(iv)
98.41°
(v)
96.41°
Question
13
13.
Two angles of a quadrilateral are of measure 120° and 81.79° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
79.10°
(ii)
78.10°
(iii)
80.10°
(iv)
77.10°
(v)
81.10°
Question
14
14.
A quadrilateral has three acute angles, each measuring 43°. What is the measure of its fourth angle?
(i)
229.00°
(ii)
230.00°
(iii)
231.00°
(iv)
233.00°
(v)
232.00°
Question
15
15.
One angle of a parallelogram measures
L
=
67.38°
.
Find the measure of each of its remaining angles.
(i)
M
=
113.62°
,
N
=
68.38°
,
O
=
113.62°
(ii)
M
=
111.62°
,
N
=
66.38°
,
O
=
111.62°
(iii)
M
=
110.62°
,
N
=
65.38°
,
O
=
110.62°
(iv)
M
=
112.62°
,
N
=
67.38°
,
O
=
112.62°
(v)
M
=
114.62°
,
N
=
69.38°
,
O
=
114.62°
Question
16
16.
Two adjacent angles of a parallelogram are in the ratio
8 : 12
.
Find the measure of each of its angles.
(i)
A
=
71°
,
B
=
106°
,
C
=
73°
,
D
=
110°
(ii)
A
=
74°
,
B
=
107°
,
C
=
70°
,
D
=
109°
(iii)
A
=
70°
,
B
=
110°
,
C
=
71°
,
D
=
109°
(iv)
A
=
73°
,
B
=
107°
,
C
=
74°
,
D
=
106°
(v)
A
=
72°
,
B
=
108°
,
C
=
72°
,
D
=
108°
Question
17
17.
In the figure given below,
CDEF
is a rectangle.
Find the values of x and y
(i)
x
=
52.13°
,
y
=
105.26°
(ii)
x
=
54.13°
,
y
=
107.26°
(iii)
x
=
53.13°
,
y
=
106.26°
(iv)
x
=
55.13°
,
y
=
108.26°
(v)
x
=
51.13°
,
y
=
104.26°
Question
18
18.
In the figure given below,
CDEF
is a rectangle.
Find the values of x and y
(i)
x
=
27.57°
,
y
=
64.43°
(ii)
x
=
25.57°
,
y
=
62.43°
(iii)
x
=
24.57°
,
y
=
61.43°
(iv)
x
=
28.57°
,
y
=
65.43°
(v)
x
=
26.57°
,
y
=
63.43°
Question
19
19.
In the figure given below,
FGHI
is a rhombus.
Find the values of x and y
(i)
x
=
28.56°
,
y
=
28.56°
(ii)
x
=
24.56°
,
y
=
24.56°
(iii)
x
=
25.56°
,
y
=
25.56°
(iv)
x
=
26.56°
,
y
=
26.56°
(v)
x
=
27.56°
,
y
=
27.56°
Question
20
20.
In the figure given below,
FGHI
is a rhombus.
Find the values of x and y
(i)
x
=
24.34°
,
y
=
24.34°
(ii)
x
=
25.34°
,
y
=
25.34°
(iii)
x
=
26.34°
,
y
=
26.34°
(iv)
x
=
22.34°
,
y
=
22.34°
(v)
x
=
23.34°
,
y
=
23.34°
Question
21
21.
In the figure given below,
KLMN
is a rhombus.
Find the values of x and y
(i)
x
=
56.67°
,
y
=
37.33°
(ii)
x
=
53.67°
,
y
=
34.33°
(iii)
x
=
54.67°
,
y
=
35.33°
(iv)
x
=
55.67°
,
y
=
36.33°
(v)
x
=
52.67°
,
y
=
33.33°
Question
22
22.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
H
=
58°
,
I
=
122°
,
J
=
59°
,
K
=
121°
(ii)
H
=
59°
,
I
=
118°
,
J
=
61°
,
K
=
122°
(iii)
H
=
62°
,
I
=
119°
,
J
=
58°
,
K
=
121°
(iv)
H
=
60°
,
I
=
120°
,
J
=
60°
,
K
=
120°
(v)
H
=
61°
,
I
=
119°
,
J
=
62°
,
K
=
118°
Question
23
23.
In the adjoining figure,
PQRS
is a trapezium in which
PQ
∥
RS
.
If
x = 61.39°
and
y = 82.23°
,
find the measures of
∠R
and
∠S
.
(i)
R
=
99.77°
,
S
=
120.61°
(ii)
R
=
98.77°
,
S
=
119.61°
(iii)
R
=
97.77°
,
S
=
118.61°
(iv)
R
=
95.77°
,
S
=
116.61°
(v)
R
=
96.77°
,
S
=
117.61°
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 = 23.59° and ∠ABO = 68.12°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 66.41° , b = 22.88° , c = 68.12° , d = 66.41° , e = 23.59°
(ii)
a = 66.41° , b = 21.88° , c = 68.12° , d = 66.41° , e = 23.59°
(iii)
a = 66.41° , b = 22.88° , c = 67.12° , d = 68.41° , e = 21.59°
(iv)
a = 66.41° , b = 22.88° , c = 67.12° , d = 66.41° , e = 23.59°
(v)
a = 66.41° , b = 22.88° , c = 67.12° , d = 68.41° , e = 23.59°
Question
25
25.
In the adjoining figure, side IJ of parallelogram GHIJ has been produced to K. If ∠HIK = 161.39° , find the measure of each angle of the parallelogram.
(i)
G
=
19.61°
,
H
=
160.39°
,
I
=
20.61°
,
J
=
159.39°
(ii)
G
=
17.61°
,
H
=
159.39°
,
I
=
19.61°
,
J
=
163.39°
(iii)
G
=
18.61°
,
H
=
161.39°
,
I
=
18.61°
,
J
=
161.39°
(iv)
G
=
16.61°
,
H
=
163.39°
,
I
=
17.61°
,
J
=
162.39°
(v)
G
=
20.61°
,
H
=
160.39°
,
I
=
16.61°
,
J
=
162.39°
Question
26
26.
In the adjoining figure,
DEFG
is a parallelogram and
HI
is such that
HI
∥
DF
If
∠DGH = 53.02°
and
∠FGI = 48.51°
,
find the measure of
∠FGD
.
(i)
79.47°
(ii)
80.47°
(iii)
77.47°
(iv)
76.47°
(v)
78.47°
Question
27
27.
In the adjoining figure, NOPQ is a square. A line segment QS cuts the side OP at S and the diagonal NP at R such that ∠QRP = 104.48° and ∠RSP = x°. Find the value of x .
(i)
58.48°
(ii)
60.48°
(iii)
59.48°
(iv)
57.48°
(v)
61.48°
Question
28
28.
In the adjoining figure, CDEF is a rhombus and △GFE is an equilateral triangle. G and D are on opposite sides of EF. If ∠FCD = 69.63°, find the values of x and y .
(i)
x
=
28°
,
y
=
23.19°
(ii)
x
=
32°
,
y
=
27.19°
(iii)
x
=
29°
,
y
=
24.19°
(iv)
x
=
30°
,
y
=
25.19°
(v)
x
=
31°
,
y
=
26.19°
Question
29
29.
In the adjoining figure, equilateral △QPR surmounts square NOPQ. If PRN = x°, find the value of x.
(i)
44°
(ii)
47°
(iii)
43°
(iv)
45°
(v)
46°
Question
30
30.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
4 : 11
,
find the angles of
△OAB
.
(i)
O
=
92°
,
A
=
24°
,
B
=
64°
(ii)
O
=
90°
,
A
=
24°
,
B
=
66°
(iii)
O
=
88°
,
A
=
26°
,
B
=
66°
(iv)
O
=
90°
,
A
=
22°
,
B
=
68°
(v)
O
=
88°
,
A
=
24°
,
B
=
68°
Question
31
31.
In the given figure,
JKLM
is a rectangle whose diagonals intersect at
N
.
Diagonal
JL
is produced to
T
and
∠KJT =
138.37°
. Find the angles of
△NKL
.
(i)
N
=
81.26°
,
K
=
48.37°
,
L
=
50.37°
(ii)
N
=
85.26°
,
K
=
48.37°
,
L
=
46.37°
(iii)
N
=
83.26°
,
K
=
46.37°
,
L
=
50.37°
(iv)
N
=
83.26°
,
K
=
48.37°
,
L
=
48.37°
(v)
N
=
81.26°
,
K
=
50.37°
,
L
=
48.37°
Question
32
32.
In the given figure,
OPQR
is a kite whose diagonals intersect at
S
.
If
∠PQR = 67.94°
and
∠QRO = 115.79°
, calculate
∠SOP
and
∠QSP
.
(i)
x
=
29.24°
,
y
=
89°
(ii)
x
=
32.24°
,
y
=
92°
(iii)
x
=
31.24°
,
y
=
91°
(iv)
x
=
28.24°
,
y
=
88°
(v)
x
=
30.24°
,
y
=
90°
Question
33
33.
△QPM
is an equilateral triangle in a square
MNOP
.
If
MO
and
QP
intersect at
R
,
then find the value of x.
(i)
75°
(ii)
77°
(iii)
76°
(iv)
73°
(v)
74°
Question
34
34.
In the adjoining figure,
Q
is a point in the interior of
∠SOT
.
If
QP
⟂
OS
and
QR
⟂
OT
and
∠SOT = 55°
,
find the measure of x .
(i)
234°
(ii)
235°
(iii)
236°
(iv)
233°
(v)
237°
Question
35
35.
Find the missing angle in the given quadrilateral
(i)
105.18°
(ii)
85.18°
(iii)
80.18°
(iv)
90.18°
(v)
75.18°
Question
36
36.
Find the missing angle in the given trapezium
(i)
106.06°
(ii)
116.06°
(iii)
111.06°
(iv)
131.06°
(v)
101.06°
Question
37
37.
Find the missing angle in the given parallelogram
(i)
71.39°
(ii)
66.39°
(iii)
76.39°
(iv)
91.39°
(v)
61.39°
Question
38
38.
Find the missing angle in the given rhombus
(i)
116.7°
(ii)
121.7°
(iii)
131.7°
(iv)
126.7°
(v)
146.7°
Question
39
39.
In the given figure, CDEF is a parallelogram.
If
CU
and
DU
are bisector of
∠C
&
∠D
, find
∠U
(i)
89°
(ii)
88°
(iii)
90°
(iv)
91°
(v)
92°
Question
40
40.
In the given figure, ABCD is a parallelogram. U is the mid-point of CD.
BU
bisects
∠B
. If x =
52°
, find angle 'y'.
(i)
38°
(ii)
36°
(iii)
40°
(iv)
39°
(v)
37°
Question
41
41.
In the given figure, BCDE is a quadrilateral. QE and QD are bisectors of ∠E & ∠D meeting at Q. Find ∠DQE
(i)
87.5°
(ii)
88.5°
(iii)
89.5°
(iv)
91.5°
(v)
90.5°
Question
42
42.
In the given figure, CDEF is a rhombus. Given x = 54°, find the value of 'y'.
(i)
35°
(ii)
36°
(iii)
34°
(iv)
37°
(v)
38°
Question
43
43.
In the given figure, BCDE is a parallelogram. BD bisects ∠B & ∠D.
Given
BD = 15 cm
and
CE = 10 cm
, find
BC
(i)
8.01 cm
(ii)
10.01 cm
(iii)
11.01 cm
(iv)
9.01 cm
(v)
7.01 cm
Question
44
44.
In the given figure, IJKL is a parallelogram. JL is the diagonal
such that
IL = JL = JK
. Given
∠I = 58°
, find
∠LJK
(i)
66°
(ii)
64°
(iii)
65°
(iv)
62°
(v)
63°
Question
45
45.
In the given figure, DEFG is a parallelogram. DR and FS are perpendicular to the diagonal EG. Given ∠RDE = 20°, find ∠FGE
(i)
71°
(ii)
70°
(iii)
68°
(iv)
69°
(v)
72°
Question
46
46.
In the given figure, ABCD is a rhombus such that ∠B = 120°. Then △ABD is
(i)
Obtuse angled triangle
(ii)
Equilateral triangle
(iii)
Isosceles triangle
(iv)
Right angled triangle
Question
47
47.
P, Q, R are the mid-points of the sides of triangle EFG.
If the perimeter of the
△EFG
is
51 cm
, the perimeter of
△PQR
is
(i)
25.5 cm
(ii)
27.5 cm
(iii)
24.5 cm
(iv)
23.5 cm
(v)
26.5 cm
Question
48
48.
DEFG is a rhombus. P, Q, R and S are mid-points of sides DE, EF, FG and GD. Find ∠QRS
(i)
90°
(ii)
89°
(iii)
88°
(iv)
92°
(v)
91°
Question
49
49.
In the given figure, IJKL is a parallelogram
such that
M
and
N
are mid-points of sides
IJ
&
KL
.
IN
meets
JL
at
P
and
KM
meets
JL
at
Q
. Given
JL
=
18 cm
, find
JQ
(i)
4.00 cm
(ii)
5.00 cm
(iii)
8.00 cm
(iv)
6.00 cm
(v)
7.00 cm
Question
50
50.
In the given figure, EFGH is a parallelogram such that R is the mid-point of EF and EF = 2HE. Find ∠HRG
(i)
91°
(ii)
88°
(iii)
89°
(iv)
90°
(v)
92°
Question
51
51.
DEFG is an isosceles trapezium. DQ and EQ are angular bisector of ∠D & ∠E. If ∠D = 68°, find ∠DQE
(i)
111°
(ii)
112°
(iii)
114°
(iv)
113°
(v)
110°
Question
52
52.
In the given figure, HIJK is a parallelogram. The bisector of the angles H, I, J & K intersect at P, Q, R & S to form a quadrilateral. Find ∠SPQ
(i)
88°
(ii)
92°
(iii)
91°
(iv)
90°
(v)
89°
Assignment Key
1) (iv)
2) (v)
3) (i)
4) (iii)
5) (iv)
6) (iv)
7) (v)
8) (i)
9) (ii)
10) (iv)
11) (v)
12) (iv)
13) (i)
14) (iii)
15) (iv)
16) (v)
17) (iii)
18) (v)
19) (iv)
20) (i)
21) (iii)
22) (iv)
23) (iii)
24) (ii)
25) (iii)
26) (v)
27) (iii)
28) (iv)
29) (iv)
30) (ii)
31) (iv)
32) (v)
33) (i)
34) (ii)
35) (v)
36) (v)
37) (v)
38) (i)
39) (iii)
40) (i)
41) (iii)
42) (ii)
43) (iv)
44) (ii)
45) (ii)
46) (ii)
47) (i)
48) (i)
49) (iv)
50) (iv)
51) (ii)
52) (iv)
