EduSahara™ Assignment
Name : Quadrilateral Angle Properties
Chapter : Quadrilaterals
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In parallelogram ABCD, if ∠B = 150.07°, then find the value of ∠A
(i)
28.93°
(ii)
29.93°
(iii)
27.93°
(iv)
31.93°
(v)
30.93°
Question
2
2.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
91°
(ii)
88°
(iii)
90°
(iv)
92°
(v)
89°
Question
3
3.
The sum of the interior angles of a quadrilateral is
(i)
90°
(ii)
270°
(iii)
360°
(iv)
180°
Question
4
4.
The angles of a quadrilateral ABCD are in the ratio 1 : 2 : 3 : 6. Find the measure of each angle of the quadrilateral.
(i)
A
=
29°
,
B
=
58°
,
C
=
91°
,
D
=
182°
(ii)
A
=
32°
,
B
=
59°
,
C
=
88°
,
D
=
181°
(iii)
A
=
30°
,
B
=
60°
,
C
=
90°
,
D
=
180°
(iv)
A
=
31°
,
B
=
59°
,
C
=
92°
,
D
=
178°
(v)
A
=
28°
,
B
=
62°
,
C
=
89°
,
D
=
181°
Question
5
5.
Two adjacent angles of a parallelogram KLMN are in the ratio 10 : 80. Find the measure of each of its angles.
(i)
K
=
21°
,
L
=
159°
,
M
=
22°
,
N
=
158°
(ii)
K
=
22°
,
L
=
159°
,
M
=
18°
,
N
=
161°
(iii)
K
=
20°
,
L
=
160°
,
M
=
20°
,
N
=
160°
(iv)
K
=
19°
,
L
=
158°
,
M
=
21°
,
N
=
162°
(v)
K
=
18°
,
L
=
162°
,
M
=
19°
,
N
=
161°
Question
6
6.
In the adjoining figure,
FGHI
is a parallelogram in which
∠IFH = 26.63°
,
∠HFG = 16.34°
,
∠IJH = 125.47°
. Calculate
∠FGI
(i)
37.19°
(ii)
40.19°
(iii)
38.19°
(iv)
39.19°
(v)
36.19°
Question
7
7.
In the adjoining figure,
MNOP
is a parallelogram in which
∠PMO = 26.96°
,
∠OMN = 51.49°
,
∠PQO = 59.67°
. Calculate
∠OPN
(i)
67.84°
(ii)
68.84°
(iii)
70.84°
(iv)
66.84°
(v)
69.84°
Question
8
8.
In the adjoining figure,
KLMN
is a parallelogram in which
∠NKM = 24.97°
,
∠MKL = 33.2°
,
∠NOM = 71.75°
. Calculate
∠LMK
(i)
25.97°
(ii)
23.97°
(iii)
24.97°
(iv)
26.97°
(v)
22.97°
Question
9
9.
In the adjoining figure,
FGHI
is a parallelogram in which
∠IFH = 54.36°
,
∠HFG = 29.36°
,
∠IJH = 116.97°
. Calculate
∠IGH
(i)
61.61°
(ii)
64.61°
(iii)
62.61°
(iv)
63.61°
(v)
60.61°
Question
10
10.
In the adjoining figure,
DEFG
is a rectangle.
If
∠FDE = 48.58°
, find
∠DEG
(i)
50.58°
(ii)
48.58°
(iii)
46.58°
(iv)
47.58°
(v)
49.58°
Question
11
11.
Three angles of quadrilateral measure 113.84°, 92.12° and 70.53° respectively. Find the measure of the fourth angle
(i)
83.51°
(ii)
85.51°
(iii)
81.51°
(iv)
82.51°
(v)
84.51°
Question
12
12.
Three angles of a quadrilateral are equal and the fourth angle measure 108.21°. What is the measure of each of the equal angles?
(i)
82.93°
(ii)
85.93°
(iii)
81.93°
(iv)
84.93°
(v)
83.93°
Question
13
13.
Two angles of a quadrilateral are of measure 67.12° and 99.37° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
96.75°
(ii)
94.75°
(iii)
98.75°
(iv)
97.75°
(v)
95.75°
Question
14
14.
A quadrilateral has three acute angles, each measuring 77°. What is the measure of its fourth angle?
(i)
129.00°
(ii)
128.00°
(iii)
130.00°
(iv)
131.00°
(v)
127.00°
Question
15
15.
One angle of a parallelogram measures
K
=
58.67°
.
Find the measure of each of its remaining angles.
(i)
L
=
120.33°
,
M
=
57.67°
,
N
=
120.33°
(ii)
L
=
119.33°
,
M
=
56.67°
,
N
=
119.33°
(iii)
L
=
121.33°
,
M
=
58.67°
,
N
=
121.33°
(iv)
L
=
122.33°
,
M
=
59.67°
,
N
=
122.33°
(v)
L
=
123.33°
,
M
=
60.67°
,
N
=
123.33°
Question
16
16.
Two adjacent angles of a parallelogram are in the ratio
30 : 60
.
Find the measure of each of its angles.
(i)
A
=
61°
,
B
=
119°
,
C
=
62°
,
D
=
118°
(ii)
A
=
60°
,
B
=
120°
,
C
=
60°
,
D
=
120°
(iii)
A
=
59°
,
B
=
118°
,
C
=
61°
,
D
=
122°
(iv)
A
=
62°
,
B
=
119°
,
C
=
58°
,
D
=
121°
(v)
A
=
58°
,
B
=
122°
,
C
=
59°
,
D
=
121°
Question
17
17.
In the figure given below,
BCDE
is a rectangle.
Find the values of x and y
(i)
x
=
47.49°
,
y
=
94.98°
(ii)
x
=
46.49°
,
y
=
93.98°
(iii)
x
=
49.49°
,
y
=
96.98°
(iv)
x
=
48.49°
,
y
=
95.98°
(v)
x
=
45.49°
,
y
=
92.98°
Question
18
18.
In the figure given below,
ABCD
is a rectangle.
Find the values of x and y
(i)
x
=
41.26°
,
y
=
44.74°
(ii)
x
=
42.26°
,
y
=
45.74°
(iii)
x
=
43.26°
,
y
=
46.74°
(iv)
x
=
45.26°
,
y
=
48.74°
(v)
x
=
44.26°
,
y
=
47.74°
Question
19
19.
In the figure given below,
MNOP
is a rhombus.
Find the values of x and y
(i)
x
=
47.98°
,
y
=
47.98°
(ii)
x
=
48.98°
,
y
=
48.98°
(iii)
x
=
45.98°
,
y
=
45.98°
(iv)
x
=
44.98°
,
y
=
44.98°
(v)
x
=
46.98°
,
y
=
46.98°
Question
20
20.
In the figure given below,
MNOP
is a rhombus.
Find the values of x and y
(i)
x
=
52.71°
,
y
=
52.71°
(ii)
x
=
51.71°
,
y
=
51.71°
(iii)
x
=
54.71°
,
y
=
54.71°
(iv)
x
=
50.71°
,
y
=
50.71°
(v)
x
=
53.71°
,
y
=
53.71°
Question
21
21.
In the figure given below,
DEFG
is a rhombus.
Find the values of x and y
(i)
x
=
24.48°
,
y
=
67.52°
(ii)
x
=
23.48°
,
y
=
66.52°
(iii)
x
=
21.48°
,
y
=
64.52°
(iv)
x
=
25.48°
,
y
=
68.52°
(v)
x
=
22.48°
,
y
=
65.52°
Question
22
22.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
A
=
62°
,
B
=
119°
,
C
=
58°
,
D
=
121°
(ii)
A
=
58°
,
B
=
122°
,
C
=
59°
,
D
=
121°
(iii)
A
=
59°
,
B
=
118°
,
C
=
61°
,
D
=
122°
(iv)
A
=
61°
,
B
=
119°
,
C
=
62°
,
D
=
118°
(v)
A
=
60°
,
B
=
120°
,
C
=
60°
,
D
=
120°
Question
23
23.
In the adjoining figure,
PQRS
is a trapezium in which
PQ
∥
RS
.
If
x = 104.5°
and
y = 117.35°
,
find the measures of
∠P
and
∠Q
.
(i)
P
=
63.65°
,
Q
=
76.5°
(ii)
P
=
60.65°
,
Q
=
73.5°
(iii)
P
=
61.65°
,
Q
=
74.5°
(iv)
P
=
64.65°
,
Q
=
77.5°
(v)
P
=
62.65°
,
Q
=
75.5°
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 = 36.37° and ∠ABO = 64.14°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 53.63° , b = 26.86° , c = 64.14° , d = 53.63° , e = 36.37°
(ii)
a = 53.63° , b = 26.86° , c = 63.14° , d = 55.63° , e = 36.37°
(iii)
a = 53.63° , b = 26.86° , c = 63.14° , d = 55.63° , e = 34.37°
(iv)
a = 53.63° , b = 26.86° , c = 63.14° , d = 53.63° , e = 36.37°
(v)
a = 53.63° , b = 25.86° , c = 64.14° , d = 53.63° , e = 36.37°
Question
25
25.
In the adjoining figure, side QN of parallelogram NOPQ has been produced to R. If ∠ONR = 117.42° , find the measure of each angle of the parallelogram.
(i)
N
=
61.58°
,
O
=
115.42°
,
P
=
63.58°
,
Q
=
119.42°
(ii)
N
=
63.58°
,
O
=
116.42°
,
P
=
64.58°
,
Q
=
115.42°
(iii)
N
=
64.58°
,
O
=
116.42°
,
P
=
60.58°
,
Q
=
118.42°
(iv)
N
=
62.58°
,
O
=
117.42°
,
P
=
62.58°
,
Q
=
117.42°
(v)
N
=
60.58°
,
O
=
119.42°
,
P
=
61.58°
,
Q
=
118.42°
Question
26
26.
In the adjoining figure,
NOPQ
is a parallelogram and
RS
is such that
RS
∥
NP
If
∠NQR = 19.97°
and
∠PQS = 26.14°
,
find the measure of
∠PQN
.
(i)
135.89°
(ii)
131.89°
(iii)
133.89°
(iv)
134.89°
(v)
132.89°
Question
27
27.
In the adjoining figure, KLMN is a square. A line segment NP cuts the side LM at P and the diagonal KM at O such that ∠NOM = 109.62° and ∠OPM = x°. Find the value of x .
(i)
66.62°
(ii)
62.62°
(iii)
65.62°
(iv)
64.62°
(v)
63.62°
Question
28
28.
In the adjoining figure, KLMN is a rhombus and △ONM is an equilateral triangle. O and L are on opposite sides of MN. If ∠NKL = 79°, find the values of x and y .
(i)
x
=
31°
,
y
=
21.5°
(ii)
x
=
28°
,
y
=
18.5°
(iii)
x
=
32°
,
y
=
22.5°
(iv)
x
=
30°
,
y
=
20.5°
(v)
x
=
29°
,
y
=
19.5°
Question
29
29.
In the adjoining figure, equilateral △KJL surmounts square HIJK. If JLI = x°, find the value of x.
(i)
17°
(ii)
13°
(iii)
14°
(iv)
15°
(v)
16°
Question
30
30.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
7 : 8
,
find the angles of
△OAB
.
(i)
O
=
90°
,
A
=
40°
,
B
=
50°
(ii)
O
=
90°
,
A
=
42°
,
B
=
48°
(iii)
O
=
92°
,
A
=
42°
,
B
=
46°
(iv)
O
=
88°
,
A
=
44°
,
B
=
48°
(v)
O
=
88°
,
A
=
42°
,
B
=
50°
Question
31
31.
In the given figure,
EFGH
is a rectangle whose diagonals intersect at
I
.
Diagonal
FH
is produced to
T
and
∠EHT =
130.92°
. Find the angles of
△IFG
.
(i)
I
=
79.84°
,
F
=
51.08°
,
G
=
49.08°
(ii)
I
=
81.84°
,
F
=
49.08°
,
G
=
49.08°
(iii)
I
=
81.84°
,
F
=
47.08°
,
G
=
51.08°
(iv)
I
=
79.84°
,
F
=
49.08°
,
G
=
51.08°
(v)
I
=
83.84°
,
F
=
49.08°
,
G
=
47.08°
Question
32
32.
In the given figure,
LMNO
is a kite whose diagonals intersect at
P
.
If
∠MNO = 78.63°
and
∠NOL = 105.95°
, calculate
∠PLM
and
∠NPM
.
(i)
x
=
36.74°
,
y
=
92°
(ii)
x
=
34.74°
,
y
=
90°
(iii)
x
=
32.74°
,
y
=
88°
(iv)
x
=
35.74°
,
y
=
91°
(v)
x
=
33.74°
,
y
=
89°
Question
33
33.
△TQR
is an equilateral triangle in a square
PQRS
.
If
PR
and
TQ
intersect at
U
,
then find the value of x.
(i)
73°
(ii)
76°
(iii)
75°
(iv)
74°
(v)
77°
Question
34
34.
In the adjoining figure,
D
is a point in the interior of
∠FBG
.
If
DC
⟂
BF
and
DE
⟂
BG
and
∠FBG = 38°
,
find the measure of x .
(i)
144°
(ii)
142°
(iii)
141°
(iv)
143°
(v)
140°
Question
35
35.
Find the missing angle in the given quadrilateral
(i)
140.68°
(ii)
160.68°
(iii)
130.68°
(iv)
135.68°
(v)
145.68°
Question
36
36.
Find the missing angle in the given trapezium
(i)
153.69°
(ii)
128.69°
(iii)
133.69°
(iv)
123.69°
(v)
138.69°
Question
37
37.
Find the missing angle in the given parallelogram
(i)
141.02°
(ii)
121.02°
(iii)
116.02°
(iv)
111.02°
(v)
126.02°
Question
38
38.
Find the missing angle in the given rhombus
(i)
82.69°
(ii)
87.69°
(iii)
77.69°
(iv)
72.69°
(v)
102.69°
Question
39
39.
In the given figure, BCDE is a parallelogram.
If
BU
and
CU
are bisector of
∠B
&
∠C
, find
∠U
(i)
89°
(ii)
92°
(iii)
91°
(iv)
88°
(v)
90°
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)
36°
(iii)
38°
(iv)
37°
(v)
40°
Question
41
41.
In the given figure, HIJK is a quadrilateral. RK and RJ are bisectors of ∠K & ∠J meeting at R. Find ∠JRK
(i)
97.5°
(ii)
94.5°
(iii)
96.5°
(iv)
95.5°
(v)
93.5°
Question
42
42.
In the given figure, FGHI is a rhombus. Given x = 51°, find the value of 'y'.
(i)
41°
(ii)
38°
(iii)
40°
(iv)
39°
(v)
37°
Question
43
43.
In the given figure, DEFG is a parallelogram. DF bisects ∠D & ∠F.
Given
DF = 9 cm
and
EG = 6 cm
, find
DE
(i)
4.41 cm
(ii)
3.41 cm
(iii)
7.41 cm
(iv)
6.41 cm
(v)
5.41 cm
Question
44
44.
In the given figure, EFGH is a parallelogram. FH is the diagonal
such that
EH = FH = FG
. Given
∠E = 49°
, find
∠HFG
(i)
81°
(ii)
83°
(iii)
82°
(iv)
80°
(v)
84°
Question
45
45.
In the given figure, BCDE is a parallelogram. BN and DO are perpendicular to the diagonal CE. Given ∠ODE = 33°, find ∠ECB
(i)
58°
(ii)
57°
(iii)
59°
(iv)
56°
(v)
55°
Question
46
46.
In the given figure, GHIJ is a rhombus such that ∠H = 120°. Then △GHJ is
(i)
Equilateral triangle
(ii)
Right angled triangle
(iii)
Isosceles triangle
(iv)
Obtuse angled triangle
Question
47
47.
R, S, T are the mid-points of the sides of triangle EFG.
If the perimeter of the
△EFG
is
51 cm
, the perimeter of
△RST
is
(i)
25.5 cm
(ii)
24.5 cm
(iii)
26.5 cm
(iv)
23.5 cm
(v)
27.5 cm
Question
48
48.
ABCD is a rhombus. N, O, P and Q are mid-points of sides AB, BC, CD and DA. Find ∠OPQ
(i)
90°
(ii)
89°
(iii)
92°
(iv)
88°
(v)
91°
Question
49
49.
In the given figure, EFGH is a parallelogram
such that
I
and
J
are mid-points of sides
EF
&
GH
.
EJ
meets
FH
at
S
and
GI
meets
FH
at
T
. Given
FH
=
20 cm
, find
ST
(i)
4.67 cm
(ii)
8.67 cm
(iii)
6.67 cm
(iv)
7.67 cm
(v)
5.67 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)
88°
(ii)
91°
(iii)
89°
(iv)
92°
(v)
90°
Question
51
51.
EFGH is an isosceles trapezium. ES and FS are angular bisector of ∠E & ∠F. If ∠E = 64°, find ∠ESF
(i)
114°
(ii)
118°
(iii)
117°
(iv)
116°
(v)
115°
Question
52
52.
In the given figure, BCDE is a parallelogram. The bisector of the angles B, C, D & E intersect at S, T, U & V to form a quadrilateral. Find ∠STU
(i)
92°
(ii)
89°
(iii)
88°
(iv)
91°
(v)
90°
Assignment Key
1) (ii)
2) (iii)
3) (iii)
4) (iii)
5) (iii)
6) (iii)
7) (ii)
8) (iii)
9) (iii)
10) (ii)
11) (i)
12) (v)
13) (i)
14) (i)
15) (iii)
16) (ii)
17) (i)
18) (iii)
19) (v)
20) (i)
21) (ii)
22) (v)
23) (v)
24) (v)
25) (iv)
26) (iii)
27) (iv)
28) (iv)
29) (iv)
30) (ii)
31) (ii)
32) (ii)
33) (iii)
34) (ii)
35) (iii)
36) (iv)
37) (iv)
38) (iv)
39) (v)
40) (iii)
41) (iv)
42) (iv)
43) (v)
44) (iii)
45) (ii)
46) (i)
47) (i)
48) (i)
49) (iii)
50) (v)
51) (iv)
52) (v)
