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
62.52°
,
128.66°
and
63.03°
. Find the fourth angle
(i)
105.79°
(ii)
110.79°
(iii)
115.79°
(iv)
120.79°
(v)
135.79°
Question
2
2.
Find the missing angle in the given quadrilateral
(i)
109.93°
(ii)
139.93°
(iii)
119.93°
(iv)
124.93°
(v)
114.93°
Question
3
3.
Find the missing angle in the given trapezium
(i)
120.69°
(ii)
115.69°
(iii)
105.69°
(iv)
110.69°
(v)
135.69°
Question
4
4.
Find the missing angle in the given rhombus
(i)
83.74°
(ii)
88.74°
(iii)
73.74°
(iv)
103.74°
(v)
78.74°
Question
5
5.
In parallelogram ABCD, if ∠B = 134.43°, then find the value of ∠D
(i)
134.43°
(ii)
132.43°
(iii)
136.43°
(iv)
133.43°
(v)
135.43°
Question
6
6.
If the opposite angles of a parallelogram are supplementary, the measure of each of its angles is
(i)
88°
(ii)
91°
(iii)
90°
(iv)
92°
(v)
89°
Question
7
7.
The sum of the interior angles of a quadrilateral is
(i)
270°
(ii)
360°
(iii)
90°
(iv)
180°
Question
8
8.
If ABCD is an isosceles trapezium, ∠D =
(i)
90°
(ii)
∠B
(iii)
∠C
(iv)
∠A
Question
9
9.
CDEF is a rhombus in which ∠C = 120° .
DF
is the diagonal. Then △CDE is
(i)
an equilateral triangle
(ii)
a scalene triangle
(iii)
None of these
(iv)
an isosceles triangle
(v)
an obtuse angled triangle
Question
10
10.
PQRS is a rhombus in which ∠P = 122° .
QS
is the diagonal. Then △PQR is
(i)
a scalene triangle
(ii)
an equilateral triangle
(iii)
an isosceles triangle
(iv)
None of these
(v)
an obtuse angled triangle
Question
11
11.
The angles of a quadrilateral KLMN are in the ratio 6 : 4 : 12 : 18. Find the measure of each angle of the quadrilateral.
(i)
K
=
55°
,
L
=
35°
,
M
=
110°
,
N
=
160°
(ii)
K
=
56°
,
L
=
35°
,
M
=
106°
,
N
=
163°
(iii)
K
=
54°
,
L
=
36°
,
M
=
108°
,
N
=
162°
(iv)
K
=
52°
,
L
=
38°
,
M
=
107°
,
N
=
163°
(v)
K
=
53°
,
L
=
34°
,
M
=
109°
,
N
=
164°
Question
12
12.
Two adjacent angles of a parallelogram KLMN are in the ratio 6 : 84. Find the measure of each of its angles.
(i)
K
=
14°
,
L
=
167°
,
M
=
10°
,
N
=
169°
(ii)
K
=
11°
,
L
=
166°
,
M
=
13°
,
N
=
170°
(iii)
K
=
13°
,
L
=
167°
,
M
=
14°
,
N
=
166°
(iv)
K
=
12°
,
L
=
168°
,
M
=
12°
,
N
=
168°
(v)
K
=
10°
,
L
=
170°
,
M
=
11°
,
N
=
169°
Question
13
13.
In the adjoining figure,
MNOP
is a parallelogram in which
∠PMO = 30.28°
,
∠OMN = 43.83°
,
∠PQO = 71.83°
. Calculate
∠MNP
(i)
64.34°
(ii)
65.34°
(iii)
63.34°
(iv)
62.34°
(v)
66.34°
Question
14
14.
In the adjoining figure,
MNOP
is a parallelogram in which
∠PMO = 36.52°
,
∠OMN = 40°
,
∠PQO = 85.78°
. Calculate
∠OPN
(i)
54.22°
(ii)
53.22°
(iii)
56.22°
(iv)
55.22°
(v)
52.22°
Question
15
15.
Three angles of quadrilateral measure 106.47°, 134.62° and 51.93° respectively. Find the measure of the fourth angle
(i)
65.98°
(ii)
66.98°
(iii)
68.98°
(iv)
64.98°
(v)
67.98°
Question
16
16.
Three angles of a quadrilateral are equal and the fourth angle measure 37.5°. What is the measure of each of the equal angles?
(i)
105.50°
(ii)
109.50°
(iii)
108.50°
(iv)
106.50°
(v)
107.50°
Question
17
17.
Two angles of a quadrilateral are of measure 50.75° and 145.57° respectively and the other two angles are equal. Find the measure of each of the equal angles.
(i)
79.84°
(ii)
82.84°
(iii)
80.84°
(iv)
83.84°
(v)
81.84°
Question
18
18.
A quadrilateral has three acute angles, each measuring 49°. What is the measure of its fourth angle?
(i)
211.00°
(ii)
214.00°
(iii)
215.00°
(iv)
213.00°
(v)
212.00°
Question
19
19.
One angle of a parallelogram measures
G
=
40.16°
.
Find the measure of each of its remaining angles.
(i)
H
=
137.84°
,
I
=
38.16°
,
J
=
137.84°
(ii)
H
=
138.84°
,
I
=
39.16°
,
J
=
138.84°
(iii)
H
=
139.84°
,
I
=
40.16°
,
J
=
139.84°
(iv)
H
=
141.84°
,
I
=
42.16°
,
J
=
141.84°
(v)
H
=
140.84°
,
I
=
41.16°
,
J
=
140.84°
Question
20
20.
Two adjacent angles of a parallelogram are in the ratio
4 : 14
.
Find the measure of each of its angles.
(i)
A
=
38°
,
B
=
142°
,
C
=
39°
,
D
=
141°
(ii)
A
=
41°
,
B
=
139°
,
C
=
42°
,
D
=
138°
(iii)
A
=
42°
,
B
=
139°
,
C
=
38°
,
D
=
141°
(iv)
A
=
40°
,
B
=
140°
,
C
=
40°
,
D
=
140°
(v)
A
=
39°
,
B
=
138°
,
C
=
41°
,
D
=
142°
Question
21
21.
In the figure given below,
CDEF
is a rhombus.
Find the values of x and y
(i)
x
=
22.66°
,
y
=
22.66°
(ii)
x
=
23.66°
,
y
=
23.66°
(iii)
x
=
24.66°
,
y
=
24.66°
(iv)
x
=
21.66°
,
y
=
21.66°
(v)
x
=
20.66°
,
y
=
20.66°
Question
22
22.
One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus
(i)
N
=
59°
,
O
=
118°
,
P
=
61°
,
Q
=
122°
(ii)
N
=
62°
,
O
=
119°
,
P
=
58°
,
Q
=
121°
(iii)
N
=
58°
,
O
=
122°
,
P
=
59°
,
Q
=
121°
(iv)
N
=
60°
,
O
=
120°
,
P
=
60°
,
Q
=
120°
(v)
N
=
61°
,
O
=
119°
,
P
=
62°
,
Q
=
118°
Question
23
23.
In the adjoining figure,
EFGH
is a trapezium in which
EF
∥
GH
.
If
x = 57.27°
and
y = 77.04°
,
find the measures of
∠G
and
∠H
.
(i)
G
=
102.96°
,
H
=
122.73°
(ii)
G
=
100.96°
,
H
=
120.73°
(iii)
G
=
101.96°
,
H
=
121.73°
(iv)
G
=
104.96°
,
H
=
124.73°
(v)
G
=
103.96°
,
H
=
123.73°
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
=
90°
,
A
=
28°
,
B
=
62°
(ii)
O
=
88°
,
A
=
32°
,
B
=
60°
(iii)
O
=
90°
,
A
=
30°
,
B
=
60°
(iv)
O
=
88°
,
A
=
30°
,
B
=
62°
(v)
O
=
92°
,
A
=
30°
,
B
=
58°
Question
25
25.
Find the missing angle in the given parallelogram
(i)
142.54°
(ii)
112.54°
(iii)
122.54°
(iv)
127.54°
(v)
117.54°
Question
26
26.
In the adjoining figure,
JKLM
is a parallelogram in which
∠MJL = 35.63°
,
∠LJK = 45.74°
,
∠MNL = 78.12°
. Calculate
∠KLJ
(i)
36.63°
(ii)
37.63°
(iii)
33.63°
(iv)
35.63°
(v)
34.63°
Question
27
27.
In the adjoining figure,
LMNO
is a parallelogram in which
∠OLN = 54.34°
,
∠NLM = 76.26°
,
∠OPN = 76.12°
. Calculate
∠OMN
(i)
19.78°
(ii)
20.78°
(iii)
21.78°
(iv)
23.78°
(v)
22.78°
Question
28
28.
In the adjoining figure,
GHIJ
is a rectangle.
If
∠IGH = 43.27°
, find
∠HIG
(i)
46.73°
(ii)
48.73°
(iii)
44.73°
(iv)
45.73°
(v)
47.73°
Question
29
29.
In the figure given below,
KLMN
is a rectangle.
Find the values of x and y
(i)
x
=
48.18°
,
y
=
96.36°
(ii)
x
=
46.18°
,
y
=
94.36°
(iii)
x
=
47.18°
,
y
=
95.36°
(iv)
x
=
49.18°
,
y
=
97.36°
(v)
x
=
50.18°
,
y
=
98.36°
Question
30
30.
In the figure given below,
DEFG
is a rectangle.
Find the values of x and y
(i)
x
=
47.12°
,
y
=
42.88°
(ii)
x
=
48.12°
,
y
=
43.88°
(iii)
x
=
46.12°
,
y
=
41.88°
(iv)
x
=
45.12°
,
y
=
40.88°
(v)
x
=
49.12°
,
y
=
44.88°
Question
31
31.
In the figure given below,
LMNO
is a rhombus.
Find the values of x and y
(i)
x
=
61.96°
,
y
=
61.96°
(ii)
x
=
62.96°
,
y
=
62.96°
(iii)
x
=
60.96°
,
y
=
60.96°
(iv)
x
=
63.96°
,
y
=
63.96°
(v)
x
=
64.96°
,
y
=
64.96°
Question
32
32.
In the figure given below,
GHIJ
is a rhombus.
Find the values of x and y
(i)
x
=
41.24°
,
y
=
52.76°
(ii)
x
=
39.24°
,
y
=
50.76°
(iii)
x
=
37.24°
,
y
=
48.76°
(iv)
x
=
40.24°
,
y
=
51.76°
(v)
x
=
38.24°
,
y
=
49.76°
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 = 41.76° and ∠ABO = 57.67°, find the measure of each of the angles marked a,b,c,d and e.
(i)
a = 48.24° , b = 33.33° , c = 56.67° , d = 50.24° , e = 39.76°
(ii)
a = 48.24° , b = 33.33° , c = 56.67° , d = 48.24° , e = 41.76°
(iii)
a = 48.24° , b = 33.33° , c = 56.67° , d = 50.24° , e = 41.76°
(iv)
a = 48.24° , b = 32.33° , c = 57.67° , d = 48.24° , e = 41.76°
(v)
a = 48.24° , b = 33.33° , c = 57.67° , d = 48.24° , e = 41.76°
Question
34
34.
In the adjoining figure, side MJ of parallelogram JKLM has been produced to N. If ∠KJN = 87.14° , find the measure of each angle of the parallelogram.
(i)
J
=
94.86°
,
K
=
86.14°
,
L
=
90.86°
,
M
=
88.14°
(ii)
J
=
92.86°
,
K
=
87.14°
,
L
=
92.86°
,
M
=
87.14°
(iii)
J
=
91.86°
,
K
=
85.14°
,
L
=
93.86°
,
M
=
89.14°
(iv)
J
=
90.86°
,
K
=
89.14°
,
L
=
91.86°
,
M
=
88.14°
(v)
J
=
93.86°
,
K
=
86.14°
,
L
=
94.86°
,
M
=
85.14°
Question
35
35.
In the adjoining figure,
LMNO
is a parallelogram and
PQ
is such that
PQ
∥
LN
If
∠LOP = 40.94°
and
∠NOQ = 51.93°
,
find the measure of
∠LMN
.
(i)
88.14°
(ii)
89.14°
(iii)
87.14°
(iv)
86.14°
(v)
85.14°
Question
36
36.
In the adjoining figure, DEFG is a square. A line segment GI cuts the side EF at I and the diagonal DF at H such that ∠GHF = 98.28° and ∠HIF = x°. Find the value of x .
(i)
55.28°
(ii)
54.28°
(iii)
51.28°
(iv)
52.28°
(v)
53.28°
Question
37
37.
In the adjoining figure, CDEF is a rhombus and △GFE is an equilateral triangle. G and D are on opposite sides of EF. If ∠FCD = 88.85°, find the values of x and y .
(i)
x
=
29°
,
y
=
14.58°
(ii)
x
=
32°
,
y
=
17.58°
(iii)
x
=
31°
,
y
=
16.58°
(iv)
x
=
30°
,
y
=
15.58°
(v)
x
=
28°
,
y
=
13.58°
Question
38
38.
In the adjoining figure, equilateral △NMO surmounts square KLMN. If MOK = x°, find the value of x.
(i)
43°
(ii)
47°
(iii)
45°
(iv)
46°
(v)
44°
Question
39
39.
In the given figure,
CDEF
is a rectangle whose diagonals intersect at
G
.
Diagonal
CE
is produced to
T
and
∠FET =
116.57°
. Find the angles of
△GDE
.
(i)
G
=
124.86°
,
D
=
28.57°
,
E
=
26.57°
(ii)
G
=
126.86°
,
D
=
24.57°
,
E
=
28.57°
(iii)
G
=
126.86°
,
D
=
26.57°
,
E
=
26.57°
(iv)
G
=
128.86°
,
D
=
26.57°
,
E
=
24.57°
(v)
G
=
124.86°
,
D
=
26.57°
,
E
=
28.57°
Question
40
40.
In the given figure,
GHIJ
is a kite whose diagonals intersect at
K
.
If
∠HIJ = 36.68°
and
∠IJG = 139.73°
, calculate
∠KGH
and
∠IKH
.
(i)
x
=
23.93°
,
y
=
92°
(ii)
x
=
19.93°
,
y
=
88°
(iii)
x
=
20.93°
,
y
=
89°
(iv)
x
=
22.93°
,
y
=
91°
(v)
x
=
21.93°
,
y
=
90°
Question
41
41.
△OLM
is an equilateral triangle in a square
KLMN
.
If
KM
and
OL
intersect at
P
,
then find the value of x.
(i)
76°
(ii)
75°
(iii)
77°
(iv)
73°
(v)
74°
Question
42
42.
In the adjoining figure,
P
is a point in the interior of
∠RNS
.
If
PO
⟂
NR
and
PQ
⟂
NS
and
∠RNS = 43°
,
find the measure of x .
(i)
139°
(ii)
138°
(iii)
137°
(iv)
135°
(v)
136°
Question
43
43.
In the given figure, DEFG is a rhombus. Given x = 54°, find the value of 'y'.
(i)
34°
(ii)
38°
(iii)
35°
(iv)
36°
(v)
37°
Question
44
44.
In the given figure, FGHI is a parallelogram. FH bisects ∠F & ∠H.
Given
FH = 9 cm
and
GI = 6 cm
, find
FG
(i)
5.41 cm
(ii)
6.41 cm
(iii)
3.41 cm
(iv)
7.41 cm
(v)
4.41 cm
Question
45
45.
In the given figure, FGHI is a parallelogram. GI is the diagonal
such that
FI = GI = GH
. Given
∠F = 64°
, find
∠IGH
(i)
52°
(ii)
50°
(iii)
51°
(iv)
53°
(v)
54°
Question
46
46.
In the given figure, FGHI is a parallelogram. FR and HS are perpendicular to the diagonal GI. Given ∠RFG = 30°, find ∠HIG
(i)
59°
(ii)
60°
(iii)
62°
(iv)
61°
(v)
58°
Question
47
47.
In the given figure, HIJK is a rhombus such that ∠I = 120°. Then △HIK is
(i)
Right angled triangle
(ii)
Obtuse angled triangle
(iii)
Equilateral triangle
(iv)
Isosceles triangle
Assignment Key
1) (i)
2) (i)
3) (iii)
4) (iii)
5) (i)
6) (iii)
7) (ii)
8) (iii)
9) (i)
10) (iii)
11) (iii)
12) (iv)
13) (i)
14) (i)
15) (ii)
16) (v)
17) (v)
18) (iv)
19) (iii)
20) (iv)
21) (i)
22) (iv)
23) (i)
24) (iii)
25) (ii)
26) (iv)
27) (iii)
28) (i)
29) (i)
30) (i)
31) (ii)
32) (ii)
33) (iv)
34) (ii)
35) (iii)
36) (v)
37) (iv)
38) (iii)
39) (iii)
40) (v)
41) (ii)
42) (iii)
43) (iv)
44) (i)
45) (i)
46) (ii)
47) (iii)
