EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : CBSE Grade IX
License : Non Commercial Use
Question
1
1.
The angles of a quadrilateral OPQR are in the ratio 1 : 2 : 3 : 6. Find the measure of each angle of the quadrilateral.
(i)
O
=
28°
,
P
=
62°
,
Q
=
89°
,
R
=
181°
(ii)
O
=
30°
,
P
=
60°
,
Q
=
90°
,
R
=
180°
(iii)
O
=
29°
,
P
=
58°
,
Q
=
91°
,
R
=
182°
(iv)
O
=
32°
,
P
=
59°
,
Q
=
88°
,
R
=
181°
(v)
O
=
31°
,
P
=
59°
,
Q
=
92°
,
R
=
178°
Question
2
2.
Two adjacent angles of a parallelogram PQRS are in the ratio 7 : 23. Find the measure of each of its angles.
(i)
P
=
40°
,
Q
=
140°
,
R
=
41°
,
S
=
139°
(ii)
P
=
43°
,
Q
=
137°
,
R
=
44°
,
S
=
136°
(iii)
P
=
42°
,
Q
=
138°
,
R
=
42°
,
S
=
138°
(iv)
P
=
44°
,
Q
=
137°
,
R
=
40°
,
S
=
139°
(v)
P
=
41°
,
Q
=
136°
,
R
=
43°
,
S
=
140°
Question
3
3.
In the adjoining figure,
MNOP
is a parallelogram in which
∠PMO = 21.51°
,
∠OMN = 41.67°
,
∠PQO = 54.74°
. Calculate
∠MNP
(i)
82.59°
(ii)
83.59°
(iii)
81.59°
(iv)
85.59°
(v)
84.59°
Question
4
4.
In the adjoining figure,
CDEF
is a parallelogram in which
∠FCE = 19.35°
,
∠ECD = 23.11°
,
∠FGE = 74.59°
. Calculate
∠EFD
(i)
80.30°
(ii)
84.30°
(iii)
82.30°
(iv)
83.30°
(v)
81.30°
Question
5
5.
In the adjoining figure,
LMNO
is a parallelogram in which
∠OLN = 23.04°
,
∠NLM = 24°
,
∠OPN = 85.65°
. Calculate
∠MNL
(i)
22.04°
(ii)
23.04°
(iii)
25.04°
(iv)
24.04°
(v)
21.04°
Question
6
6.
In the adjoining figure,
OPQR
is a parallelogram in which
∠ROQ = 48.54°
,
∠QOP = 54.09°
,
∠RSQ = 85.45°
. Calculate
∠RPQ
(i)
37.91°
(ii)
36.91°
(iii)
34.91°
(iv)
35.91°
(v)
38.91°
Question
7
7.
In the adjoining figure,
JKLM
is a rectangle.
If
∠LJK = 49.9°
, find
∠JKM
(i)
48.90°
(ii)
51.90°
(iii)
49.90°
(iv)
47.90°
(v)
50.90°
Question
8
8.
Three angles of quadrilateral measure 106.88°, 109.55° and 82.29° respectively. Find the measure of the fourth angle
(i)
63.28°
(ii)
60.28°
(iii)
62.28°
(iv)
61.28°
(v)
59.28°
Question
9
9.
Three angles of a quadrilateral are equal and the fourth angle measure 57.91°. What is the measure of each of the equal angles?
(i)
102.70°
(ii)
99.70°
(iii)
98.70°
(iv)
101.70°
(v)
100.70°
Question
10
10.
Two angles of a quadrilateral are of measure 110.74° and 81.38° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
83.94°
(ii)
81.94°
(iii)
84.94°
(iv)
82.94°
(v)
85.94°
Question
11
11.
A quadrilateral has three acute angles, each measuring 57°. What is the measure of its fourth angle?
(i)
187.00°
(ii)
191.00°
(iii)
189.00°
(iv)
188.00°
(v)
190.00°
Question
12
12.
One angle of a parallelogram measures
J
=
57.12°
.
Find the measure of each of its remaining angles.
(i)
K
=
124.88°
,
L
=
59.12°
,
M
=
124.88°
(ii)
K
=
121.88°
,
L
=
56.12°
,
M
=
121.88°
(iii)
K
=
122.88°
,
L
=
57.12°
,
M
=
122.88°
(iv)
K
=
123.88°
,
L
=
58.12°
,
M
=
123.88°
(v)
K
=
120.88°
,
L
=
55.12°
,
M
=
120.88°
Question
13
13.
Two adjacent angles of a parallelogram are in the ratio
12 : 18
.
Find the measure of each of its angles.
(i)
A
=
73°
,
B
=
107°
,
C
=
74°
,
D
=
106°
(ii)
A
=
74°
,
B
=
107°
,
C
=
70°
,
D
=
109°
(iii)
A
=
72°
,
B
=
108°
,
C
=
72°
,
D
=
108°
(iv)
A
=
70°
,
B
=
110°
,
C
=
71°
,
D
=
109°
(v)
A
=
71°
,
B
=
106°
,
C
=
73°
,
D
=
110°
Question
14
14.
In the figure given below,
PQRS
is a rectangle.
Find the values of x and y
(i)
x
=
41.24°
,
y
=
81.48°
(ii)
x
=
39.24°
,
y
=
79.48°
(iii)
x
=
40.24°
,
y
=
80.48°
(iv)
x
=
42.24°
,
y
=
82.48°
(v)
x
=
38.24°
,
y
=
78.48°
Question
15
15.
In the figure given below,
NOPQ
is a rectangle.
Find the values of x and y
(i)
x
=
28.96°
,
y
=
57.04°
(ii)
x
=
29.96°
,
y
=
58.04°
(iii)
x
=
32.96°
,
y
=
61.04°
(iv)
x
=
31.96°
,
y
=
60.04°
(v)
x
=
30.96°
,
y
=
59.04°
Question
16
16.
In the figure given below,
ABCD
is a rhombus.
Find the values of x and y
(i)
x
=
54.13°
,
y
=
54.13°
(ii)
x
=
55.13°
,
y
=
55.13°
(iii)
x
=
53.13°
,
y
=
53.13°
(iv)
x
=
51.13°
,
y
=
51.13°
(v)
x
=
52.13°
,
y
=
52.13°
Question
17
17.
In the figure given below,
OPQR
is a rhombus.
Find the values of x and y
(i)
x
=
25.34°
,
y
=
25.34°
(ii)
x
=
23.34°
,
y
=
23.34°
(iii)
x
=
26.34°
,
y
=
26.34°
(iv)
x
=
22.34°
,
y
=
22.34°
(v)
x
=
24.34°
,
y
=
24.34°
Question
18
18.
In the figure given below,
CDEF
is a rhombus.
Find the values of x and y
(i)
x
=
34.87°
,
y
=
51.13°
(ii)
x
=
36.87°
,
y
=
53.13°
(iii)
x
=
37.87°
,
y
=
54.13°
(iv)
x
=
38.87°
,
y
=
55.13°
(v)
x
=
35.87°
,
y
=
52.13°
Question
19
19.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
M
=
58°
,
N
=
122°
,
O
=
59°
,
P
=
121°
(ii)
M
=
61°
,
N
=
119°
,
O
=
62°
,
P
=
118°
(iii)
M
=
60°
,
N
=
120°
,
O
=
60°
,
P
=
120°
(iv)
M
=
62°
,
N
=
119°
,
O
=
58°
,
P
=
121°
(v)
M
=
59°
,
N
=
118°
,
O
=
61°
,
P
=
122°
Question
20
20.
In the adjoining figure,
EFGH
is a trapezium in which
EF
∥
GH
.
If
x = 42.41°
and
y = 68.6°
,
find the measures of
∠G
and
∠H
.
(i)
G
=
113.4°
,
H
=
139.59°
(ii)
G
=
110.4°
,
H
=
136.59°
(iii)
G
=
111.4°
,
H
=
137.59°
(iv)
G
=
109.4°
,
H
=
135.59°
(v)
G
=
112.4°
,
H
=
138.59°
Question
21
21.
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 = 47.16° and ∠ABO = 59.26°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 42.84° , b = 31.74° , c = 58.26° , d = 44.84° , e = 47.16°
(ii)
a = 42.84° , b = 31.74° , c = 59.26° , d = 42.84° , e = 47.16°
(iii)
a = 42.84° , b = 30.74° , c = 59.26° , d = 42.84° , e = 47.16°
(iv)
a = 42.84° , b = 31.74° , c = 58.26° , d = 44.84° , e = 45.16°
(v)
a = 42.84° , b = 31.74° , c = 58.26° , d = 42.84° , e = 47.16°
Question
22
22.
In the adjoining figure, side LM of parallelogram KLMN has been produced to O. If ∠KLO = 28.89° , find the measure of each angle of the parallelogram.
(i)
K
=
28.89°
,
L
=
151.11°
,
M
=
28.89°
,
N
=
151.11°
(ii)
K
=
29.89°
,
L
=
150.11°
,
M
=
30.89°
,
N
=
149.11°
(iii)
K
=
30.89°
,
L
=
150.11°
,
M
=
26.89°
,
N
=
152.11°
(iv)
K
=
26.89°
,
L
=
153.11°
,
M
=
27.89°
,
N
=
152.11°
(v)
K
=
27.89°
,
L
=
149.11°
,
M
=
29.89°
,
N
=
153.11°
Question
23
23.
In the adjoining figure,
OPQR
is a parallelogram and
ST
is such that
ST
∥
OQ
If
∠ORS = 40.85°
and
∠QRT = 34.08°
,
find the measure of
∠QRO
.
(i)
107.07°
(ii)
104.07°
(iii)
105.07°
(iv)
106.07°
(v)
103.07°
Question
24
24.
In the adjoining figure, LMNO is a square. A line segment OQ cuts the side MN at Q and the diagonal LN at P such that ∠OPN = 106.45° and ∠PQN = x°. Find the value of x .
(i)
60.45°
(ii)
59.45°
(iii)
62.45°
(iv)
63.45°
(v)
61.45°
Question
25
25.
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 = 73.74°, find the values of x and y .
(i)
x
=
32°
,
y
=
25.13°
(ii)
x
=
28°
,
y
=
21.13°
(iii)
x
=
30°
,
y
=
23.13°
(iv)
x
=
31°
,
y
=
24.13°
(v)
x
=
29°
,
y
=
22.13°
Question
26
26.
In the adjoining figure, equilateral △DCE surmounts square ABCD. If CEB = x°, find the value of x.
(i)
15°
(ii)
13°
(iii)
14°
(iv)
16°
(v)
17°
Question
27
27.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
1 : 2
,
find the angles of
△OAB
.
(i)
O
=
90°
,
A
=
28°
,
B
=
62°
(ii)
O
=
90°
,
A
=
30°
,
B
=
60°
(iii)
O
=
88°
,
A
=
30°
,
B
=
62°
(iv)
O
=
92°
,
A
=
30°
,
B
=
58°
(v)
O
=
88°
,
A
=
32°
,
B
=
60°
Question
28
28.
In the given figure,
KLMN
is a rectangle whose diagonals intersect at
O
.
Diagonal
KM
is produced to
T
and
∠LKT =
118.07°
. Find the angles of
△ONK
.
(i)
O
=
123.86°
,
N
=
28.07°
,
K
=
28.07°
(ii)
O
=
121.86°
,
N
=
30.07°
,
K
=
28.07°
(iii)
O
=
121.86°
,
N
=
28.07°
,
K
=
30.07°
(iv)
O
=
123.86°
,
N
=
26.07°
,
K
=
30.07°
(v)
O
=
125.86°
,
N
=
28.07°
,
K
=
26.07°
Question
29
29.
In the given figure,
OPQR
is a kite whose diagonals intersect at
S
.
If
∠ROP = 82.85°
and
∠OPQ = 106.57°
, calculate
∠SRO
and
∠SQR
.
(i)
x
=
49.57°
,
y
=
33°
(ii)
x
=
50.57°
,
y
=
34°
(iii)
x
=
46.57°
,
y
=
30°
(iv)
x
=
48.57°
,
y
=
32°
(v)
x
=
47.57°
,
y
=
31°
Question
30
30.
△ROP
is an equilateral triangle in a square
NOPQ
.
If
OQ
and
PR
intersect at
S
,
then find the value of x.
(i)
75°
(ii)
77°
(iii)
74°
(iv)
76°
(v)
73°
Question
31
31.
In the adjoining figure,
D
is a point in the interior of
∠FBG
.
If
DC
⟂
BF
and
DE
⟂
BG
and
∠FBG = 31°
,
find the measure of x .
(i)
149°
(ii)
151°
(iii)
150°
(iv)
148°
(v)
147°
Question
32
32.
The measures of three angles of a quadrilateral are
49.32°
,
136.13°
and
47.91°
. Find the fourth angle
(i)
156.64°
(ii)
136.64°
(iii)
131.64°
(iv)
141.64°
(v)
126.64°
Question
33
33.
Sum of the interior angles in a quadrilateral is
(i)
360°
(ii)
370°
(iii)
390°
(iv)
375°
(v)
365°
Question
34
34.
How many diagonals does a quadrilateral have?
(i)
2
(ii)
0
(iii)
4
(iv)
3
(v)
1
Question
35
35.
Find the missing angle in the given quadrilateral
(i)
124.89°
(ii)
114.89°
(iii)
109.89°
(iv)
139.89°
(v)
119.89°
Question
36
36.
Find the missing angle in the given trapezium
(i)
128.61°
(ii)
133.61°
(iii)
123.61°
(iv)
118.61°
(v)
148.61°
Question
37
37.
Find the missing angle in the given parallelogram
(i)
50.89°
(ii)
60.89°
(iii)
55.89°
(iv)
80.89°
(v)
65.89°
Question
38
38.
Find the missing angle in the given rhombus
(i)
64.07°
(ii)
79.07°
(iii)
94.07°
(iv)
74.07°
(v)
69.07°
Question
39
39.
In the given figure, BCDE is a parallelogram.
If
BP
and
CP
are bisector of
∠B
&
∠C
, find
∠P
(i)
92°
(ii)
89°
(iii)
91°
(iv)
88°
(v)
90°
Question
40
40.
In the given figure, GHIJ is a parallelogram. R is the mid-point of IJ.
HR
bisects
∠H
. If x =
52°
, find angle 'y'.
(i)
40°
(ii)
37°
(iii)
39°
(iv)
36°
(v)
38°
Question
41
41.
In the given figure, ABCD is a quadrilateral. RD and RC are bisectors of ∠D & ∠C meeting at R. Find ∠CRD
(i)
88.0°
(ii)
87.0°
(iii)
90.0°
(iv)
86.0°
(v)
89.0°
Question
42
42.
In the given figure, DEFG is a rhombus. Given x = 48°, find the value of 'y'.
(i)
44°
(ii)
41°
(iii)
43°
(iv)
42°
(v)
40°
Question
43
43.
In the given figure, BCDE is a parallelogram. BD bisects ∠B & ∠D.
Given
BD = 12 cm
and
CE = 8 cm
, find
BC
(i)
5.21 cm
(ii)
7.21 cm
(iii)
8.21 cm
(iv)
6.21 cm
(v)
9.21 cm
Question
44
44.
In the given figure, GHIJ is a parallelogram. HJ is the diagonal
such that
GJ = HJ = HI
. Given
∠G = 63°
, find
∠JHI
(i)
54°
(ii)
52°
(iii)
55°
(iv)
56°
(v)
53°
Question
45
45.
In the given figure, FGHI is a parallelogram. FM and HN are perpendicular to the diagonal GI. Given ∠NHI = 32°, find ∠IGF
(i)
59°
(ii)
58°
(iii)
56°
(iv)
60°
(v)
57°
Question
46
46.
In the given figure, FGHI is a rhombus such that ∠G = 120°. Then △FGI is
(i)
Isosceles triangle
(ii)
Right angled triangle
(iii)
Equilateral triangle
(iv)
Obtuse angled triangle
Question
47
47.
EFGH is a rhombus. P, Q, R and S are mid-points of sides EF, FG, GH and HE. Find ∠QRS
(i)
90°
(ii)
89°
(iii)
91°
(iv)
88°
(v)
92°
Question
48
48.
In the given figure, FGHI is a parallelogram such that R is the mid-point of FG and FG = 2IF. Find ∠IRH
(i)
92°
(ii)
89°
(iii)
90°
(iv)
91°
(v)
88°
Assignment Key
1) (ii)
2) (iii)
3) (ii)
4) (iii)
5) (ii)
6) (ii)
7) (iii)
8) (iv)
9) (v)
10) (i)
11) (iii)
12) (iii)
13) (iii)
14) (iii)
15) (v)
16) (iii)
17) (v)
18) (ii)
19) (iii)
20) (iii)
21) (iii)
22) (i)
23) (iii)
24) (v)
25) (iii)
26) (i)
27) (ii)
28) (i)
29) (iv)
30) (i)
31) (i)
32) (v)
33) (i)
34) (i)
35) (iii)
36) (iv)
37) (i)
38) (i)
39) (v)
40) (v)
41) (i)
42) (iv)
43) (ii)
44) (i)
45) (ii)
46) (iii)
47) (i)
48) (iii)
