EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : CBSE Grade IX
License : Non Commercial Use
Question
1
1.
The angles of a quadrilateral BCDE are in the ratio 9 : 4 : 7 : 16. Find the measure of each angle of the quadrilateral.
(i)
B
=
92°
,
C
=
39°
,
D
=
68°
,
E
=
161°
(ii)
B
=
88°
,
C
=
42°
,
D
=
69°
,
E
=
161°
(iii)
B
=
90°
,
C
=
40°
,
D
=
70°
,
E
=
160°
(iv)
B
=
91°
,
C
=
39°
,
D
=
72°
,
E
=
158°
(v)
B
=
89°
,
C
=
38°
,
D
=
71°
,
E
=
162°
Question
2
2.
Two adjacent angles of a parallelogram KLMN are in the ratio 2 : 10. Find the measure of each of its angles.
(i)
K
=
32°
,
L
=
149°
,
M
=
28°
,
N
=
151°
(ii)
K
=
31°
,
L
=
149°
,
M
=
32°
,
N
=
148°
(iii)
K
=
30°
,
L
=
150°
,
M
=
30°
,
N
=
150°
(iv)
K
=
29°
,
L
=
148°
,
M
=
31°
,
N
=
152°
(v)
K
=
28°
,
L
=
152°
,
M
=
29°
,
N
=
151°
Question
3
3.
In the adjoining figure,
LMNO
is a parallelogram in which
∠OLN = 32.29°
,
∠NLM = 22.89°
,
∠OPN = 110.23°
. Calculate
∠LMO
(i)
47.88°
(ii)
48.88°
(iii)
46.88°
(iv)
45.88°
(v)
44.88°
Question
4
4.
In the adjoining figure,
NOPQ
is a parallelogram in which
∠QNP = 22.27°
,
∠PNO = 18.06°
,
∠QRP = 107.36°
. Calculate
∠PQO
(i)
54.58°
(ii)
56.58°
(iii)
53.58°
(iv)
52.58°
(v)
55.58°
Question
5
5.
In the adjoining figure,
PQRS
is a parallelogram in which
∠SPR = 40.51°
,
∠RPQ = 31.5°
,
∠STR = 103.26°
. Calculate
∠QRP
(i)
40.51°
(ii)
42.51°
(iii)
41.51°
(iv)
38.51°
(v)
39.51°
Question
6
6.
In the adjoining figure,
MNOP
is a parallelogram in which
∠PMO = 37.84°
,
∠OMN = 22.27°
,
∠PQO = 118.61°
. Calculate
∠PNO
(i)
82.77°
(ii)
79.77°
(iii)
80.77°
(iv)
78.77°
(v)
81.77°
Question
7
7.
In the adjoining figure,
OPQR
is a rectangle.
If
∠QOP = 38.29°
, find
∠QSP
(i)
77.58°
(ii)
74.58°
(iii)
75.58°
(iv)
78.58°
(v)
76.58°
Question
8
8.
Three angles of quadrilateral measure 114.2°, 39.08° and 68.9° respectively. Find the measure of the fourth angle
(i)
135.82°
(ii)
137.82°
(iii)
139.82°
(iv)
136.82°
(v)
138.82°
Question
9
9.
Three angles of a quadrilateral are equal and the fourth angle measure 84.26°. What is the measure of each of the equal angles?
(i)
90.91°
(ii)
89.91°
(iii)
93.91°
(iv)
91.91°
(v)
92.91°
Question
10
10.
Two angles of a quadrilateral are of measure 92.12° and 73.45° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
98.22°
(ii)
95.22°
(iii)
96.22°
(iv)
97.22°
(v)
99.22°
Question
11
11.
A quadrilateral has three acute angles, each measuring 39°. What is the measure of its fourth angle?
(i)
241.00°
(ii)
242.00°
(iii)
244.00°
(iv)
245.00°
(v)
243.00°
Question
12
12.
One angle of a parallelogram measures
E
=
76.33°
.
Find the measure of each of its remaining angles.
(i)
F
=
102.67°
,
G
=
75.33°
,
H
=
102.67°
(ii)
F
=
105.67°
,
G
=
78.33°
,
H
=
105.67°
(iii)
F
=
104.67°
,
G
=
77.33°
,
H
=
104.67°
(iv)
F
=
103.67°
,
G
=
76.33°
,
H
=
103.67°
(v)
F
=
101.67°
,
G
=
74.33°
,
H
=
101.67°
Question
13
13.
Two adjacent angles of a parallelogram are in the ratio
9 : 9
.
Find the measure of each of its angles.
(i)
A
=
90°
,
B
=
90°
,
C
=
90°
,
D
=
90°
(ii)
A
=
92°
,
B
=
89°
,
C
=
88°
,
D
=
91°
(iii)
A
=
89°
,
B
=
88°
,
C
=
91°
,
D
=
92°
(iv)
A
=
91°
,
B
=
89°
,
C
=
92°
,
D
=
88°
(v)
A
=
88°
,
B
=
92°
,
C
=
89°
,
D
=
91°
Question
14
14.
In the figure given below,
KLMN
is a rectangle.
Find the values of x and y
(i)
x
=
51.2°
,
y
=
101.4°
(ii)
x
=
52.2°
,
y
=
102.4°
(iii)
x
=
50.2°
,
y
=
100.4°
(iv)
x
=
48.2°
,
y
=
98.4°
(v)
x
=
49.2°
,
y
=
99.4°
Question
15
15.
In the figure given below,
LMNO
is a rectangle.
Find the values of x and y
(i)
x
=
47.74°
,
y
=
44.26°
(ii)
x
=
48.74°
,
y
=
45.26°
(iii)
x
=
45.74°
,
y
=
42.26°
(iv)
x
=
46.74°
,
y
=
43.26°
(v)
x
=
44.74°
,
y
=
41.26°
Question
16
16.
In the figure given below,
HIJK
is a rhombus.
Find the values of x and y
(i)
x
=
53.25°
,
y
=
53.25°
(ii)
x
=
51.25°
,
y
=
51.25°
(iii)
x
=
54.25°
,
y
=
54.25°
(iv)
x
=
52.25°
,
y
=
52.25°
(v)
x
=
50.25°
,
y
=
50.25°
Question
17
17.
In the figure given below,
JKLM
is a rhombus.
Find the values of x and y
(i)
x
=
66.29°
,
y
=
66.29°
(ii)
x
=
70.29°
,
y
=
70.29°
(iii)
x
=
67.29°
,
y
=
67.29°
(iv)
x
=
68.29°
,
y
=
68.29°
(v)
x
=
69.29°
,
y
=
69.29°
Question
18
18.
In the figure given below,
MNOP
is a rhombus.
Find the values of x and y
(i)
x
=
37.29°
,
y
=
52.71°
(ii)
x
=
36.29°
,
y
=
51.71°
(iii)
x
=
39.29°
,
y
=
54.71°
(iv)
x
=
35.29°
,
y
=
50.71°
(v)
x
=
38.29°
,
y
=
53.71°
Question
19
19.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
N
=
62°
,
O
=
119°
,
P
=
58°
,
Q
=
121°
(ii)
N
=
58°
,
O
=
122°
,
P
=
59°
,
Q
=
121°
(iii)
N
=
59°
,
O
=
118°
,
P
=
61°
,
Q
=
122°
(iv)
N
=
60°
,
O
=
120°
,
P
=
60°
,
Q
=
120°
(v)
N
=
61°
,
O
=
119°
,
P
=
62°
,
Q
=
118°
Question
20
20.
In the adjoining figure,
NOPQ
is a trapezium in which
NO
∥
PQ
.
If
x = 103.66°
and
y = 124.67°
,
find the measures of
∠N
and
∠O
.
(i)
N
=
55.33°
,
O
=
76.34°
(ii)
N
=
57.33°
,
O
=
78.34°
(iii)
N
=
53.33°
,
O
=
74.34°
(iv)
N
=
56.33°
,
O
=
77.34°
(v)
N
=
54.33°
,
O
=
75.34°
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 = 33.97° and ∠ABO = 62.82°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 56.03° , b = 27.18° , c = 62.82° , d = 56.03° , e = 33.97°
(ii)
a = 56.03° , b = 28.18° , c = 61.82° , d = 58.03° , e = 33.97°
(iii)
a = 56.03° , b = 28.18° , c = 62.82° , d = 56.03° , e = 33.97°
(iv)
a = 56.03° , b = 28.18° , c = 61.82° , d = 56.03° , e = 33.97°
(v)
a = 56.03° , b = 28.18° , c = 61.82° , d = 58.03° , e = 31.97°
Question
22
22.
In the adjoining figure, side EB of parallelogram BCDE has been produced to F. If ∠DEF = 51.09° , find the measure of each angle of the parallelogram.
(i)
B
=
51.09°
,
C
=
128.91°
,
D
=
51.09°
,
E
=
128.91°
(ii)
B
=
50.09°
,
C
=
126.91°
,
D
=
52.09°
,
E
=
130.91°
(iii)
B
=
53.09°
,
C
=
127.91°
,
D
=
49.09°
,
E
=
129.91°
(iv)
B
=
49.09°
,
C
=
130.91°
,
D
=
50.09°
,
E
=
129.91°
(v)
B
=
52.09°
,
C
=
127.91°
,
D
=
53.09°
,
E
=
126.91°
Question
23
23.
In the adjoining figure,
ABCD
is a parallelogram and
EF
is such that
EF
∥
AC
If
∠ADE = 32.75°
and
∠CDF = 26.5°
,
find the measure of
∠CDA
.
(i)
118.76°
(ii)
121.76°
(iii)
119.76°
(iv)
120.76°
(v)
122.76°
Question
24
24.
In the adjoining figure, HIJK is a square. A line segment KM cuts the side IJ at M and the diagonal HJ at L such that ∠KLJ = 90.76° and ∠LMJ = x°. Find the value of x .
(i)
46.76°
(ii)
45.76°
(iii)
47.76°
(iv)
44.76°
(v)
43.76°
Question
25
25.
In the adjoining figure, BCDE is a rhombus and △FED is an equilateral triangle. F and C are on opposite sides of DE. If ∠EBC = 64.54°, find the values of x and y .
(i)
x
=
31°
,
y
=
28.73°
(ii)
x
=
29°
,
y
=
26.73°
(iii)
x
=
28°
,
y
=
25.73°
(iv)
x
=
32°
,
y
=
29.73°
(v)
x
=
30°
,
y
=
27.73°
Question
26
26.
In the adjoining figure, equilateral △NMO surmounts square KLMN. If MOL = x°, find the value of x.
(i)
14°
(ii)
17°
(iii)
16°
(iv)
13°
(v)
15°
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
=
88°
,
A
=
32°
,
B
=
60°
(ii)
O
=
90°
,
A
=
30°
,
B
=
60°
(iii)
O
=
90°
,
A
=
28°
,
B
=
62°
(iv)
O
=
88°
,
A
=
30°
,
B
=
62°
(v)
O
=
92°
,
A
=
30°
,
B
=
58°
Question
28
28.
In the given figure,
NOPQ
is a rectangle whose diagonals intersect at
R
.
Diagonal
OQ
is produced to
T
and
∠POT =
119.06°
. Find the angles of
△RQN
.
(i)
R
=
58.12°
,
Q
=
60.94°
,
N
=
60.94°
(ii)
R
=
60.12°
,
Q
=
60.94°
,
N
=
58.94°
(iii)
R
=
56.12°
,
Q
=
60.94°
,
N
=
62.94°
(iv)
R
=
58.12°
,
Q
=
58.94°
,
N
=
62.94°
(v)
R
=
56.12°
,
Q
=
62.94°
,
N
=
60.94°
Question
29
29.
In the given figure,
HIJK
is a kite whose diagonals intersect at
L
.
If
∠KHI = 65.74°
and
∠HIJ = 110.76°
, calculate
∠LKH
and
∠LJK
.
(i)
x
=
55.13°
,
y
=
34.37°
(ii)
x
=
58.13°
,
y
=
37.37°
(iii)
x
=
56.13°
,
y
=
35.37°
(iv)
x
=
57.13°
,
y
=
36.37°
(v)
x
=
59.13°
,
y
=
38.37°
Question
30
30.
△ONK
is an equilateral triangle in a square
KLMN
.
If
LN
and
KO
intersect at
P
,
then find the value of x.
(i)
76°
(ii)
74°
(iii)
73°
(iv)
77°
(v)
75°
Question
31
31.
In the adjoining figure,
M
is a point in the interior of
∠OKP
.
If
ML
⟂
KO
and
MN
⟂
KP
and
∠OKP = 37°
,
find the measure of x .
(i)
216°
(ii)
219°
(iii)
215°
(iv)
218°
(v)
217°
Question
32
32.
The measures of three angles of a quadrilateral are
57.61°
,
105.52°
and
70.81°
. Find the fourth angle
(i)
131.06°
(ii)
136.06°
(iii)
141.06°
(iv)
156.06°
(v)
126.06°
Question
33
33.
Sum of the interior angles in a quadrilateral is
(i)
375°
(ii)
360°
(iii)
370°
(iv)
390°
(v)
365°
Question
34
34.
How many diagonals does a quadrilateral have?
(i)
1
(ii)
4
(iii)
3
(iv)
0
(v)
2
Question
35
35.
Find the missing angle in the given quadrilateral
(i)
106.52°
(ii)
116.52°
(iii)
111.52°
(iv)
131.52°
(v)
101.52°
Question
36
36.
Find the missing angle in the given trapezium
(i)
123.93°
(ii)
108.93°
(iii)
98.93°
(iv)
93.93°
(v)
103.93°
Question
37
37.
Find the missing angle in the given parallelogram
(i)
93.95°
(ii)
73.95°
(iii)
78.95°
(iv)
63.95°
(v)
68.95°
Question
38
38.
Find the missing angle in the given rhombus
(i)
93.47°
(ii)
78.47°
(iii)
83.47°
(iv)
88.47°
(v)
108.47°
Question
39
39.
In the given figure, FGHI is a parallelogram.
If
FU
and
GU
are bisector of
∠F
&
∠G
, find
∠U
(i)
91°
(ii)
90°
(iii)
88°
(iv)
89°
(v)
92°
Question
40
40.
In the given figure, CDEF is a parallelogram. R is the mid-point of EF.
DR
bisects
∠D
. If x =
52°
, find angle 'y'.
(i)
40°
(ii)
37°
(iii)
36°
(iv)
39°
(v)
38°
Question
41
41.
In the given figure, FGHI is a quadrilateral. QI and QH are bisectors of ∠I & ∠H meeting at Q. Find ∠HQI
(i)
88.5°
(ii)
86.5°
(iii)
85.5°
(iv)
84.5°
(v)
87.5°
Question
42
42.
In the given figure, FGHI is a rhombus. Given x = 58°, find the value of 'y'.
(i)
32°
(ii)
30°
(iii)
33°
(iv)
34°
(v)
31°
Question
43
43.
In the given figure, DEFG is a parallelogram. DF bisects ∠D & ∠F.
Given
DF = 12 cm
and
EG = 8 cm
, find
DE
(i)
9.21 cm
(ii)
8.21 cm
(iii)
6.21 cm
(iv)
7.21 cm
(v)
5.21 cm
Question
44
44.
In the given figure, EFGH is a parallelogram. FH is the diagonal
such that
EH = FH = FG
. Given
∠E = 54°
, find
∠HFG
(i)
74°
(ii)
73°
(iii)
72°
(iv)
71°
(v)
70°
Question
45
45.
In the given figure, FGHI is a parallelogram. FR and HS are perpendicular to the diagonal GI. Given ∠SHI = 19°, find ∠IGF
(i)
71°
(ii)
69°
(iii)
70°
(iv)
73°
(v)
72°
Question
46
46.
In the given figure, HIJK is a rhombus such that ∠I = 120°. Then △HIK is
(i)
Isosceles triangle
(ii)
Obtuse angled triangle
(iii)
Right angled triangle
(iv)
Equilateral triangle
Question
47
47.
DEFG is a rhombus. N, O, P and Q are mid-points of sides DE, EF, FG and GD. Find ∠OPQ
(i)
88°
(ii)
90°
(iii)
91°
(iv)
92°
(v)
89°
Question
48
48.
In the given figure, HIJK is a parallelogram such that S is the mid-point of HI and HI = 2KH. Find ∠KSJ
(i)
89°
(ii)
92°
(iii)
91°
(iv)
90°
(v)
88°
Assignment Key
1) (iii)
2) (iii)
3) (iii)
4) (i)
5) (i)
6) (iii)
7) (v)
8) (ii)
9) (iv)
10) (iv)
11) (v)
12) (iv)
13) (i)
14) (iii)
15) (iv)
16) (iv)
17) (iv)
18) (i)
19) (iv)
20) (i)
21) (i)
22) (i)
23) (iv)
24) (ii)
25) (v)
26) (v)
27) (ii)
28) (i)
29) (iv)
30) (v)
31) (v)
32) (v)
33) (ii)
34) (v)
35) (v)
36) (iv)
37) (iv)
38) (ii)
39) (ii)
40) (v)
41) (ii)
42) (i)
43) (iv)
44) (iii)
45) (i)
46) (iv)
47) (ii)
48) (iv)
