EduSahara™ Assignment
Name : Quadrilateral Angle Problems
Chapter : Quadrilaterals
Grade : SSC Grade VII
License : Non Commercial Use
Question
1
1.
The measures of three angles of a quadrilateral are
73.69°
,
100.4°
and
78.46°
. Find the fourth angle
(i)
112.45°
(ii)
137.45°
(iii)
117.45°
(iv)
107.45°
(v)
122.45°
Question
2
2.
Find the missing angle in the given quadrilateral
(i)
77.72°
(ii)
62.72°
(iii)
72.72°
(iv)
67.72°
(v)
92.72°
Question
3
3.
Find the missing angle in the given trapezium
(i)
123.65°
(ii)
133.65°
(iii)
128.65°
(iv)
118.65°
(v)
148.65°
Question
4
4.
Find the missing angle in the given rhombus
(i)
83.74°
(ii)
73.74°
(iii)
88.74°
(iv)
103.74°
(v)
78.74°
Question
5
5.
In parallelogram ABCD, if ∠C = 31.59°, then find the value of ∠B
(i)
148.41°
(ii)
149.41°
(iii)
150.41°
(iv)
147.41°
(v)
146.41°
Question
6
6.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
92°
(ii)
90°
(iii)
89°
(iv)
88°
(v)
91°
Question
7
7.
The sum of the interior angles of a quadrilateral is
(i)
90°
(ii)
270°
(iii)
360°
(iv)
180°
Question
8
8.
If ABCD is an isosceles trapezium, ∠D =
(i)
∠C
(ii)
∠A
(iii)
90°
(iv)
∠B
Question
9
9.
PQRS is a rhombus in which ∠P = 120° .
QS
is the diagonal. Then △PQR is
(i)
an isosceles triangle
(ii)
a scalene triangle
(iii)
None of these
(iv)
an equilateral triangle
(v)
an obtuse angled triangle
Question
10
10.
GHIJ is a rhombus in which ∠G = 131° .
HJ
is the diagonal. Then △GHI is
(i)
an equilateral triangle
(ii)
a scalene triangle
(iii)
an obtuse angled triangle
(iv)
an isosceles triangle
(v)
None of these
Question
11
11.
The angles of a quadrilateral KLMN are in the ratio 9 : 8 : 4 : 15. Find the measure of each angle of the quadrilateral.
(i)
K
=
92°
,
L
=
79°
,
M
=
38°
,
N
=
151°
(ii)
K
=
89°
,
L
=
78°
,
M
=
41°
,
N
=
152°
(iii)
K
=
88°
,
L
=
82°
,
M
=
39°
,
N
=
151°
(iv)
K
=
90°
,
L
=
80°
,
M
=
40°
,
N
=
150°
(v)
K
=
91°
,
L
=
79°
,
M
=
42°
,
N
=
148°
Question
12
12.
Two adjacent angles of a parallelogram BCDE are in the ratio 6 : 6. Find the measure of each of its angles.
(i)
B
=
90°
,
C
=
90°
,
D
=
90°
,
E
=
90°
(ii)
B
=
91°
,
C
=
89°
,
D
=
92°
,
E
=
88°
(iii)
B
=
92°
,
C
=
89°
,
D
=
88°
,
E
=
91°
(iv)
B
=
89°
,
C
=
88°
,
D
=
91°
,
E
=
92°
(v)
B
=
88°
,
C
=
92°
,
D
=
89°
,
E
=
91°
Question
13
13.
In the adjoining figure,
IJKL
is a parallelogram in which
∠LIK = 26.33°
,
∠KIJ = 21.16°
,
∠LMK = 105.71°
. Calculate
∠IJL
(i)
54.13°
(ii)
53.13°
(iii)
51.13°
(iv)
55.13°
(v)
52.13°
Question
14
14.
In the adjoining figure,
CDEF
is a parallelogram in which
∠FCE = 42.46°
,
∠ECD = 31.28°
,
∠FGE = 105.46°
. Calculate
∠EFD
(i)
43.26°
(ii)
41.26°
(iii)
42.26°
(iv)
44.26°
(v)
45.26°
Question
15
15.
Three angles of quadrilateral measure 95.96°, 87.95° and 58.14° respectively. Find the measure of the fourth angle
(i)
116.95°
(ii)
119.95°
(iii)
117.95°
(iv)
115.95°
(v)
118.95°
Question
16
16.
Three angles of a quadrilateral are equal and the fourth angle measure 67.38°. What is the measure of each of the equal angles?
(i)
96.54°
(ii)
98.54°
(iii)
99.54°
(iv)
95.54°
(v)
97.54°
Question
17
17.
Two angles of a quadrilateral are of measure 91.64° and 130.18° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
70.09°
(ii)
67.09°
(iii)
69.09°
(iv)
71.09°
(v)
68.09°
Question
18
18.
A quadrilateral has three acute angles, each measuring 77°. What is the measure of its fourth angle?
(i)
128.00°
(ii)
130.00°
(iii)
129.00°
(iv)
131.00°
(v)
127.00°
Question
19
19.
One angle of a parallelogram measures
J
=
63.03°
.
Find the measure of each of its remaining angles.
(i)
K
=
115.97°
,
L
=
62.03°
,
M
=
115.97°
(ii)
K
=
114.97°
,
L
=
61.03°
,
M
=
114.97°
(iii)
K
=
117.97°
,
L
=
64.03°
,
M
=
117.97°
(iv)
K
=
118.97°
,
L
=
65.03°
,
M
=
118.97°
(v)
K
=
116.97°
,
L
=
63.03°
,
M
=
116.97°
Question
20
20.
Two adjacent angles of a parallelogram are in the ratio
7 : 53
.
Find the measure of each of its angles.
(i)
A
=
23°
,
B
=
158°
,
C
=
19°
,
D
=
160°
(ii)
A
=
21°
,
B
=
159°
,
C
=
21°
,
D
=
159°
(iii)
A
=
20°
,
B
=
157°
,
C
=
22°
,
D
=
161°
(iv)
A
=
19°
,
B
=
161°
,
C
=
20°
,
D
=
160°
(v)
A
=
22°
,
B
=
158°
,
C
=
23°
,
D
=
157°
Question
21
21.
In the figure given below,
PQRS
is a rhombus.
Find the values of x and y
(i)
x
=
32.65°
,
y
=
32.65°
(ii)
x
=
30.65°
,
y
=
30.65°
(iii)
x
=
31.65°
,
y
=
31.65°
(iv)
x
=
29.65°
,
y
=
29.65°
(v)
x
=
33.65°
,
y
=
33.65°
Question
22
22.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
C
=
61°
,
D
=
119°
,
E
=
62°
,
F
=
118°
(ii)
C
=
62°
,
D
=
119°
,
E
=
58°
,
F
=
121°
(iii)
C
=
60°
,
D
=
120°
,
E
=
60°
,
F
=
120°
(iv)
C
=
58°
,
D
=
122°
,
E
=
59°
,
F
=
121°
(v)
C
=
59°
,
D
=
118°
,
E
=
61°
,
F
=
122°
Question
23
23.
In the adjoining figure,
GHIJ
is a trapezium in which
GH
∥
IJ
.
If
x = 64.6°
and
y = 71.57°
,
find the measures of
∠I
and
∠J
.
(i)
I
=
109.43°
,
J
=
116.4°
(ii)
I
=
107.43°
,
J
=
114.4°
(iii)
I
=
106.43°
,
J
=
113.4°
(iv)
I
=
108.43°
,
J
=
115.4°
(v)
I
=
110.43°
,
J
=
117.4°
Question
24
24.
In the adjoining figure,
ABCD
is a rhombus whose diagonals intersect at
O
.
If
∠OAB
:
∠ABO
=
2 : 4
,
find the angles of
△OAB
.
(i)
O
=
88°
,
A
=
30°
,
B
=
62°
(ii)
O
=
90°
,
A
=
28°
,
B
=
62°
(iii)
O
=
88°
,
A
=
32°
,
B
=
60°
(iv)
O
=
90°
,
A
=
30°
,
B
=
60°
(v)
O
=
92°
,
A
=
30°
,
B
=
58°
Question
25
25.
Find the missing angle in the given parallelogram
(i)
70.78°
(ii)
100.78°
(iii)
85.78°
(iv)
80.78°
(v)
75.78°
Question
26
26.
In the adjoining figure,
HIJK
is a parallelogram in which
∠KHJ = 42.68°
,
∠JHI = 38.45°
,
∠KLJ = 94.28°
. Calculate
∠IJH
(i)
41.68°
(ii)
44.68°
(iii)
40.68°
(iv)
42.68°
(v)
43.68°
Question
27
27.
In the adjoining figure,
MNOP
is a parallelogram in which
∠PMO = 21.16°
,
∠OMN = 25.13°
,
∠PQO = 76.17°
. Calculate
∠PNO
(i)
57.02°
(ii)
55.02°
(iii)
54.02°
(iv)
53.02°
(v)
56.02°
Question
28
28.
In the adjoining figure,
LMNO
is a rectangle.
If
∠NLM = 46.85°
, find
∠OPN
(i)
85.30°
(ii)
87.30°
(iii)
84.30°
(iv)
88.30°
(v)
86.30°
Question
29
29.
In the figure given below,
HIJK
is a rectangle.
Find the values of x and y
(i)
x
=
55.62°
,
y
=
109.24°
(ii)
x
=
52.62°
,
y
=
106.24°
(iii)
x
=
51.62°
,
y
=
105.24°
(iv)
x
=
53.62°
,
y
=
107.24°
(v)
x
=
54.62°
,
y
=
108.24°
Question
30
30.
In the figure given below,
OPQR
is a rectangle.
Find the values of x and y
(i)
x
=
44.27°
,
y
=
49.73°
(ii)
x
=
42.27°
,
y
=
47.73°
(iii)
x
=
40.27°
,
y
=
45.73°
(iv)
x
=
41.27°
,
y
=
46.73°
(v)
x
=
43.27°
,
y
=
48.73°
Question
31
31.
In the figure given below,
ABCD
is a rhombus.
Find the values of x and y
(i)
x
=
65.85°
,
y
=
65.85°
(ii)
x
=
64.85°
,
y
=
64.85°
(iii)
x
=
66.85°
,
y
=
66.85°
(iv)
x
=
63.85°
,
y
=
63.85°
(v)
x
=
62.85°
,
y
=
62.85°
Question
32
32.
In the figure given below,
IJKL
is a rhombus.
Find the values of x and y
(i)
x
=
50.88°
,
y
=
41.12°
(ii)
x
=
49.88°
,
y
=
40.12°
(iii)
x
=
47.88°
,
y
=
38.12°
(iv)
x
=
48.88°
,
y
=
39.12°
(v)
x
=
51.88°
,
y
=
42.12°
Question
33
33.
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 = 33.37° and ∠ABO = 59.8°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 56.63° , b = 31.2° , c = 59.8° , d = 56.63° , e = 33.37°
(ii)
a = 56.63° , b = 31.2° , c = 58.8° , d = 58.63° , e = 31.37°
(iii)
a = 56.63° , b = 31.2° , c = 58.8° , d = 58.63° , e = 33.37°
(iv)
a = 56.63° , b = 30.2° , c = 59.8° , d = 56.63° , e = 33.37°
(v)
a = 56.63° , b = 31.2° , c = 58.8° , d = 56.63° , e = 33.37°
Question
34
34.
In the adjoining figure, side CD of parallelogram BCDE has been produced to F. If ∠BCF = 41.4° , find the measure of each angle of the parallelogram.
(i)
B
=
41.4°
,
C
=
138.6°
,
D
=
41.4°
,
E
=
138.6°
(ii)
B
=
39.4°
,
C
=
140.6°
,
D
=
40.4°
,
E
=
139.6°
(iii)
B
=
43.4°
,
C
=
137.6°
,
D
=
39.4°
,
E
=
139.6°
(iv)
B
=
42.4°
,
C
=
137.6°
,
D
=
43.4°
,
E
=
136.6°
(v)
B
=
40.4°
,
C
=
136.6°
,
D
=
42.4°
,
E
=
140.6°
Question
35
35.
In the adjoining figure,
IJKL
is a parallelogram and
MN
is such that
MN
∥
IK
If
∠ILM = 18.03°
and
∠KLN = 18.84°
,
find the measure of
∠IJK
.
(i)
145.13°
(ii)
143.13°
(iii)
144.13°
(iv)
142.13°
(v)
141.13°
Question
36
36.
In the adjoining figure, BCDE is a square. A line segment EG cuts the side CD at G and the diagonal BD at F such that ∠EFD = 106.7° and ∠FGD = x°. Find the value of x .
(i)
59.70°
(ii)
63.70°
(iii)
60.70°
(iv)
62.70°
(v)
61.70°
Question
37
37.
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 = 90°, find the values of x and y .
(i)
x
=
29°
,
y
=
14°
(ii)
x
=
32°
,
y
=
17°
(iii)
x
=
28°
,
y
=
13°
(iv)
x
=
31°
,
y
=
16°
(v)
x
=
30°
,
y
=
15°
Question
38
38.
In the adjoining figure, equilateral △QPR surmounts square NOPQ. If PRN = x°, find the value of x.
(i)
45°
(ii)
47°
(iii)
46°
(iv)
43°
(v)
44°
Question
39
39.
In the given figure,
BCDE
is a rectangle whose diagonals intersect at
F
.
Diagonal
BD
is produced to
T
and
∠CBT =
132.88°
. Find the angles of
△FEB
.
(i)
F
=
92.24°
,
E
=
42.88°
,
B
=
44.88°
(ii)
F
=
94.24°
,
E
=
42.88°
,
B
=
42.88°
(iii)
F
=
96.24°
,
E
=
42.88°
,
B
=
40.88°
(iv)
F
=
94.24°
,
E
=
40.88°
,
B
=
44.88°
(v)
F
=
92.24°
,
E
=
44.88°
,
B
=
42.88°
Question
40
40.
In the given figure,
BCDE
is a kite whose diagonals intersect at
F
.
If
∠CDE = 64.01°
and
∠DEB = 97.8°
, calculate
∠FBC
and
∠DFC
.
(i)
x
=
51.19°
,
y
=
91°
(ii)
x
=
48.19°
,
y
=
88°
(iii)
x
=
49.19°
,
y
=
89°
(iv)
x
=
52.19°
,
y
=
92°
(v)
x
=
50.19°
,
y
=
90°
Question
41
41.
△MKL
is an equilateral triangle in a square
IJKL
.
If
JL
and
MK
intersect at
N
,
then find the value of x.
(i)
75°
(ii)
77°
(iii)
76°
(iv)
74°
(v)
73°
Question
42
42.
In the adjoining figure,
D
is a point in the interior of
∠FBG
.
If
DC
⟂
BF
and
DE
⟂
BG
and
∠FBG = 58°
,
find the measure of x .
(i)
123°
(ii)
121°
(iii)
120°
(iv)
122°
(v)
124°
Question
43
43.
In the given figure, DEFG is a rhombus. Given x = 56°, find the value of 'y'.
(i)
35°
(ii)
32°
(iii)
34°
(iv)
36°
(v)
33°
Question
44
44.
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)
9.21 cm
(iii)
7.21 cm
(iv)
6.21 cm
(v)
8.21 cm
Question
45
45.
In the given figure, KLMN is a parallelogram. LN is the diagonal
such that
KN = LN = LM
. Given
∠K = 62°
, find
∠NLM
(i)
57°
(ii)
56°
(iii)
58°
(iv)
55°
(v)
54°
Question
46
46.
In the given figure, BCDE is a parallelogram. BM and DN are perpendicular to the diagonal CE. Given ∠NDE = 39°, find ∠ECB
(i)
52°
(ii)
49°
(iii)
51°
(iv)
50°
(v)
53°
Question
47
47.
In the given figure, FGHI is a rhombus such that ∠G = 120°. Then △FGI is
(i)
Right angled triangle
(ii)
Obtuse angled triangle
(iii)
Isosceles triangle
(iv)
Equilateral triangle
Assignment Key
1) (iv)
2) (ii)
3) (iv)
4) (ii)
5) (i)
6) (ii)
7) (iii)
8) (i)
9) (iv)
10) (iv)
11) (iv)
12) (i)
13) (ii)
14) (i)
15) (iii)
16) (v)
17) (iii)
18) (iii)
19) (v)
20) (ii)
21) (iii)
22) (iii)
23) (iv)
24) (iv)
25) (i)
26) (iv)
27) (ii)
28) (v)
29) (iv)
30) (ii)
31) (ii)
32) (ii)
33) (iv)
34) (i)
35) (ii)
36) (v)
37) (v)
38) (i)
39) (ii)
40) (v)
41) (i)
42) (iv)
43) (iii)
44) (iii)
45) (ii)
46) (iii)
47) (iv)
