EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In parallelogram ABCD, if ∠C = 26.38°, then find the value of ∠B
(i)
153.62°
(ii)
152.62°
(iii)
155.62°
(iv)
154.62°
(v)
151.62°
Question
2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
92°
(ii)
89°
(iii)
90°
(iv)
88°
(v)
91°
Question
3
3.
The sum of the interior angles of a quadrilateral is
(i)
90°
(ii)
180°
(iii)
270°
(iv)
360°
Question
4
4.
The angles of a quadrilateral LMNO are in the ratio 19 : 8 : 25 : 68. Find the measure of each angle of the quadrilateral.
(i)
L
=
58°
,
M
=
23°
,
N
=
77°
,
O
=
202°
(ii)
L
=
56°
,
M
=
22°
,
N
=
76°
,
O
=
206°
(iii)
L
=
55°
,
M
=
26°
,
N
=
74°
,
O
=
205°
(iv)
L
=
59°
,
M
=
23°
,
N
=
73°
,
O
=
205°
(v)
L
=
57°
,
M
=
24°
,
N
=
75°
,
O
=
204°
Question
5
5.
Two adjacent angles of a parallelogram HIJK are in the ratio 14 : 22. Find the measure of each of its angles.
(i)
H
=
70°
,
I
=
110°
,
J
=
70°
,
K
=
110°
(ii)
H
=
71°
,
I
=
109°
,
J
=
72°
,
K
=
108°
(iii)
H
=
69°
,
I
=
108°
,
J
=
71°
,
K
=
112°
(iv)
H
=
72°
,
I
=
109°
,
J
=
68°
,
K
=
111°
(v)
H
=
68°
,
I
=
112°
,
J
=
69°
,
K
=
111°
Question
6
6.
In the adjoining figure,
ABCD
is a parallelogram in which
∠DAC = 18.89°
,
∠CAB = 12.4°
,
∠DEC = 129.12°
. Calculate
∠ABD
(i)
40.48°
(ii)
37.48°
(iii)
39.48°
(iv)
36.48°
(v)
38.48°
Question
7
7.
In the adjoining figure,
BCDE
is a parallelogram in which
∠EBD = 38.87°
,
∠DBC = 22.48°
,
∠EFD = 119.4°
. Calculate
∠DEC
(i)
37.12°
(ii)
38.12°
(iii)
39.12°
(iv)
40.12°
(v)
36.12°
Question
8
8.
In the adjoining figure,
HIJK
is a parallelogram in which
∠KHJ = 59.13°
,
∠JHI = 70.35°
,
∠KLJ = 82.4°
. Calculate
∠IJH
(i)
59.13°
(ii)
57.13°
(iii)
60.13°
(iv)
61.13°
(v)
58.13°
Question
9
9.
In the adjoining figure,
BCDE
is a parallelogram in which
∠EBD = 13.94°
,
∠DBC = 8.38°
,
∠EFD = 144.02°
. Calculate
∠ECD
(i)
131.07°
(ii)
132.07°
(iii)
130.07°
(iv)
129.07°
(v)
128.07°
Question
10
10.
In the adjoining figure,
BCDE
is a rectangle.
If
∠DBC = 53.13°
, find
∠EFD
(i)
72.74°
(ii)
73.74°
(iii)
74.74°
(iv)
75.74°
(v)
71.74°
Question
11
11.
Three angles of quadrilateral measure 50.75°, 130.44° and 94.46° respectively. Find the measure of the fourth angle
(i)
86.35°
(ii)
84.35°
(iii)
85.35°
(iv)
83.35°
(v)
82.35°
Question
12
12.
Three angles of a quadrilateral are equal and the fourth angle measure 43.28°. What is the measure of each of the equal angles?
(i)
105.57°
(ii)
103.57°
(iii)
107.57°
(iv)
106.57°
(v)
104.57°
Question
13
13.
Two angles of a quadrilateral are of measure 85.9° and 134.62° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
67.74°
(ii)
71.74°
(iii)
69.74°
(iv)
68.74°
(v)
70.74°
Question
14
14.
A quadrilateral has three acute angles, each measuring 38°. What is the measure of its fourth angle?
(i)
247.00°
(ii)
245.00°
(iii)
244.00°
(iv)
246.00°
(v)
248.00°
Question
15
15.
One angle of a parallelogram measures
M
=
57.12°
.
Find the measure of each of its remaining angles.
(i)
N
=
123.88°
,
O
=
58.12°
,
P
=
123.88°
(ii)
N
=
120.88°
,
O
=
55.12°
,
P
=
120.88°
(iii)
N
=
124.88°
,
O
=
59.12°
,
P
=
124.88°
(iv)
N
=
122.88°
,
O
=
57.12°
,
P
=
122.88°
(v)
N
=
121.88°
,
O
=
56.12°
,
P
=
121.88°
Question
16
16.
Two adjacent angles of a parallelogram are in the ratio
14 : 46
.
Find the measure of each of its angles.
(i)
A
=
44°
,
B
=
137°
,
C
=
40°
,
D
=
139°
(ii)
A
=
41°
,
B
=
136°
,
C
=
43°
,
D
=
140°
(iii)
A
=
40°
,
B
=
140°
,
C
=
41°
,
D
=
139°
(iv)
A
=
43°
,
B
=
137°
,
C
=
44°
,
D
=
136°
(v)
A
=
42°
,
B
=
138°
,
C
=
42°
,
D
=
138°
Question
17
17.
In the figure given below,
FGHI
is a rectangle.
Find the values of x and y
(i)
x
=
55.09°
,
y
=
112.18°
(ii)
x
=
56.09°
,
y
=
113.18°
(iii)
x
=
58.09°
,
y
=
115.18°
(iv)
x
=
59.09°
,
y
=
116.18°
(v)
x
=
57.09°
,
y
=
114.18°
Question
18
18.
In the figure given below,
IJKL
is a rectangle.
Find the values of x and y
(i)
x
=
54.13°
,
y
=
37.87°
(ii)
x
=
51.13°
,
y
=
34.87°
(iii)
x
=
55.13°
,
y
=
38.87°
(iv)
x
=
52.13°
,
y
=
35.87°
(v)
x
=
53.13°
,
y
=
36.87°
Question
19
19.
In the figure given below,
MNOP
is a rhombus.
Find the values of x and y
(i)
x
=
33.78°
,
y
=
33.78°
(ii)
x
=
35.78°
,
y
=
35.78°
(iii)
x
=
34.78°
,
y
=
34.78°
(iv)
x
=
37.78°
,
y
=
37.78°
(v)
x
=
36.78°
,
y
=
36.78°
Question
20
20.
In the figure given below,
LMNO
is a rhombus.
Find the values of x and y
(i)
x
=
28.26°
,
y
=
28.26°
(ii)
x
=
31.26°
,
y
=
31.26°
(iii)
x
=
32.26°
,
y
=
32.26°
(iv)
x
=
29.26°
,
y
=
29.26°
(v)
x
=
30.26°
,
y
=
30.26°
Question
21
21.
In the figure given below,
BCDE
is a rhombus.
Find the values of x and y
(i)
x
=
33.03°
,
y
=
58.97°
(ii)
x
=
31.03°
,
y
=
56.97°
(iii)
x
=
32.03°
,
y
=
57.97°
(iv)
x
=
30.03°
,
y
=
55.97°
(v)
x
=
34.03°
,
y
=
59.97°
Question
22
22.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
L
=
58°
,
M
=
122°
,
N
=
59°
,
O
=
121°
(ii)
L
=
60°
,
M
=
120°
,
N
=
60°
,
O
=
120°
(iii)
L
=
61°
,
M
=
119°
,
N
=
62°
,
O
=
118°
(iv)
L
=
59°
,
M
=
118°
,
N
=
61°
,
O
=
122°
(v)
L
=
62°
,
M
=
119°
,
N
=
58°
,
O
=
121°
Question
23
23.
In the adjoining figure,
MNOP
is a trapezium in which
MN
∥
OP
.
If
x = 106.89°
and
y = 145.99°
,
find the measures of
∠M
and
∠N
.
(i)
M
=
36.01°
,
N
=
75.11°
(ii)
M
=
33.01°
,
N
=
72.11°
(iii)
M
=
32.01°
,
N
=
71.11°
(iv)
M
=
34.01°
,
N
=
73.11°
(v)
M
=
35.01°
,
N
=
74.11°
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 = 40.95° and ∠ABO = 52.33°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 49.05° , b = 38.67° , c = 51.33° , d = 51.05° , e = 38.95°
(ii)
a = 49.05° , b = 38.67° , c = 51.33° , d = 49.05° , e = 40.95°
(iii)
a = 49.05° , b = 38.67° , c = 52.33° , d = 49.05° , e = 40.95°
(iv)
a = 49.05° , b = 37.67° , c = 52.33° , d = 49.05° , e = 40.95°
(v)
a = 49.05° , b = 38.67° , c = 51.33° , d = 51.05° , e = 40.95°
Question
25
25.
In the adjoining figure, side BC of parallelogram ABCD has been produced to E. If ∠ABE = 109.34° , find the measure of each angle of the parallelogram.
(i)
A
=
110.34°
,
B
=
69.66°
,
C
=
111.34°
,
D
=
68.66°
(ii)
A
=
108.34°
,
B
=
68.66°
,
C
=
110.34°
,
D
=
72.66°
(iii)
A
=
107.34°
,
B
=
72.66°
,
C
=
108.34°
,
D
=
71.66°
(iv)
A
=
111.34°
,
B
=
69.66°
,
C
=
107.34°
,
D
=
71.66°
(v)
A
=
109.34°
,
B
=
70.66°
,
C
=
109.34°
,
D
=
70.66°
Question
26
26.
In the adjoining figure,
ABCD
is a parallelogram and
EF
is such that
EF
∥
AC
If
∠ADE = 27.62°
and
∠CDF = 16.84°
,
find the measure of
∠ABC
.
(i)
133.54°
(ii)
135.54°
(iii)
134.54°
(iv)
136.54°
(v)
137.54°
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 = 102.95° and ∠RSP = x°. Find the value of x .
(i)
55.95°
(ii)
57.95°
(iii)
58.95°
(iv)
59.95°
(v)
56.95°
Question
28
28.
In the adjoining figure, EFGH is a rhombus and △IHG is an equilateral triangle. I and E are on opposite sides of GH. If ∠EFG = 83.29°, find the values of x and y .
(i)
x
=
18.35°
,
y
=
30°
(ii)
x
=
19.35°
,
y
=
31°
(iii)
x
=
17.35°
,
y
=
29°
(iv)
x
=
20.35°
,
y
=
32°
(v)
x
=
16.35°
,
y
=
28°
Question
29
29.
In the adjoining figure, equilateral △HGI surmounts square EFGH. If GIE = x°, find the value of x.
(i)
44°
(ii)
47°
(iii)
45°
(iv)
46°
(v)
43°
Question
30
30.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
3 : 6
,
find the angles of
△OAB
.
(i)
O
=
90°
,
A
=
28°
,
B
=
62°
(ii)
O
=
92°
,
A
=
30°
,
B
=
58°
(iii)
O
=
88°
,
A
=
30°
,
B
=
62°
(iv)
O
=
90°
,
A
=
30°
,
B
=
60°
(v)
O
=
88°
,
A
=
32°
,
B
=
60°
Question
31
31.
In the given figure,
DEFG
is a rectangle whose diagonals intersect at
H
.
Diagonal
DF
is produced to
T
and
∠EDT =
133.36°
. Find the angles of
△HFG
.
(i)
H
=
84.72°
,
F
=
46.64°
,
G
=
48.64°
(ii)
H
=
86.72°
,
F
=
44.64°
,
G
=
48.64°
(iii)
H
=
88.72°
,
F
=
46.64°
,
G
=
44.64°
(iv)
H
=
84.72°
,
F
=
48.64°
,
G
=
46.64°
(v)
H
=
86.72°
,
F
=
46.64°
,
G
=
46.64°
Question
32
32.
In the given figure,
JKLM
is a kite whose diagonals intersect at
N
.
If
∠MJK = 39.31°
and
∠KLM = 36.87°
, calculate
∠NMJ
and
∠NKL
.
(i)
x
=
72.34°
,
y
=
73.56°
(ii)
x
=
69.34°
,
y
=
70.56°
(iii)
x
=
68.34°
,
y
=
69.56°
(iv)
x
=
70.34°
,
y
=
71.56°
(v)
x
=
71.34°
,
y
=
72.56°
Question
33
33.
△ROP
is an equilateral triangle in a square
NOPQ
.
If
OQ
and
PR
intersect at
S
,
then find the value of x.
(i)
73°
(ii)
76°
(iii)
75°
(iv)
77°
(v)
74°
Question
34
34.
In the adjoining figure,
O
is a point in the interior of
∠QMR
.
If
ON
⟂
MQ
and
OP
⟂
MR
and
∠QMR = 57°
,
find the measure of x .
(i)
239°
(ii)
236°
(iii)
235°
(iv)
237°
(v)
238°
Question
35
35.
Find the missing angle in the given quadrilateral
(i)
95.18°
(ii)
65.18°
(iii)
80.18°
(iv)
75.18°
(v)
70.18°
Question
36
36.
Find the missing angle in the given trapezium
(i)
111.48°
(ii)
96.48°
(iii)
106.48°
(iv)
101.48°
(v)
126.48°
Question
37
37.
Find the missing angle in the given parallelogram
(i)
127.81°
(ii)
137.81°
(iii)
157.81°
(iv)
132.81°
(v)
142.81°
Question
38
38.
Find the missing angle in the given rhombus
(i)
133.21°
(ii)
123.21°
(iii)
128.21°
(iv)
138.21°
(v)
153.21°
Question
39
39.
In the given figure, CDEF is a parallelogram.
If
CR
and
DR
are bisector of
∠C
&
∠D
, find
∠R
(i)
89°
(ii)
91°
(iii)
92°
(iv)
88°
(v)
90°
Question
40
40.
In the given figure, ABCD is a parallelogram. P is the mid-point of CD.
BP
bisects
∠B
. If x =
52°
, find angle 'y'.
(i)
36°
(ii)
39°
(iii)
38°
(iv)
37°
(v)
40°
Question
41
41.
In the given figure, ABCD is a quadrilateral. PD and PC are bisectors of ∠D & ∠C meeting at P. Find ∠CPD
(i)
89.5°
(ii)
90.5°
(iii)
86.5°
(iv)
88.5°
(v)
87.5°
Question
42
42.
In the given figure, ABCD is a rhombus. Given x = 58°, find the value of 'y'.
(i)
30°
(ii)
34°
(iii)
32°
(iv)
33°
(v)
31°
Question
43
43.
In the given figure, EFGH is a parallelogram. EG bisects ∠E & ∠G.
Given
EG = 9 cm
and
FH = 6 cm
, find
EF
(i)
4.41 cm
(ii)
7.41 cm
(iii)
3.41 cm
(iv)
5.41 cm
(v)
6.41 cm
Question
44
44.
In the given figure, KLMN is a parallelogram. LN is the diagonal
such that
KN = LN = LM
. Given
∠K = 53°
, find
∠NLM
(i)
76°
(ii)
72°
(iii)
75°
(iv)
73°
(v)
74°
Question
45
45.
In the given figure, ABCD is a parallelogram. AR and CS are perpendicular to the diagonal BD. Given ∠RAB = 45°, find ∠CDB
(i)
44°
(ii)
43°
(iii)
45°
(iv)
47°
(v)
46°
Question
46
46.
In the given figure, DEFG is a rhombus such that ∠E = 120°. Then △DEG is
(i)
Right angled triangle
(ii)
Obtuse 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
54 cm
, the perimeter of
△PQR
is
(i)
28.0 cm
(ii)
25.0 cm
(iii)
26.0 cm
(iv)
29.0 cm
(v)
27.0 cm
Question
48
48.
BCDE is a rhombus. P, Q, R and S are mid-points of sides BC, CD, DE and EB. Find ∠QRS
(i)
89°
(ii)
90°
(iii)
88°
(iv)
91°
(v)
92°
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
=
15 cm
, find
JQ
(i)
3.00 cm
(ii)
4.00 cm
(iii)
6.00 cm
(iv)
7.00 cm
(v)
5.00 cm
Question
50
50.
In the given figure, BCDE is a parallelogram such that R is the mid-point of BC and BC = 2EB. Find ∠ERD
(i)
89°
(ii)
90°
(iii)
92°
(iv)
88°
(v)
91°
Question
51
51.
HIJK is an isosceles trapezium. HT and IT are angular bisector of ∠H & ∠I. If ∠H = 69°, find ∠HTI
(i)
112°
(ii)
111°
(iii)
113°
(iv)
109°
(v)
110°
Question
52
52.
In the given figure, HIJK is a parallelogram. The bisector of the angles H, I, J & K intersect at T, U, V & W to form a quadrilateral. Find ∠UVW
(i)
90°
(ii)
91°
(iii)
89°
(iv)
92°
(v)
88°
Assignment Key
1) (i)
2) (iii)
3) (iv)
4) (v)
5) (i)
6) (v)
7) (ii)
8) (i)
9) (iii)
10) (ii)
11) (ii)
12) (i)
13) (iii)
14) (iv)
15) (iv)
16) (v)
17) (v)
18) (v)
19) (ii)
20) (v)
21) (iii)
22) (ii)
23) (iv)
24) (iv)
25) (v)
26) (ii)
27) (ii)
28) (i)
29) (iii)
30) (iv)
31) (v)
32) (iv)
33) (iii)
34) (iv)
35) (ii)
36) (ii)
37) (i)
38) (ii)
39) (v)
40) (iii)
41) (iv)
42) (iii)
43) (iv)
44) (v)
45) (iii)
46) (iii)
47) (v)
48) (ii)
49) (v)
50) (ii)
51) (ii)
52) (i)
