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Byju's Answer
Standard IX
Mathematics
Each Angle of a Rectangle Is 90
In the follow...
Question
In the following figure ABCD and PQRS are parallelograms. Find the measure of x in degrees.
50
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Solution
The correct option is
A
50
In the parallelogram ABCD,
∠
A
B
C
+
∠
B
A
D
= 180
∘
[sum of adjacent angles of a parallelogram is 180
∘
]
∠
A
B
C
= 180
∘
− 120
∘
= 60
∘
Similarly, in parallelogram PQRS
∠
P
Q
R
=
∠
P
S
R
= 70
∘
[Opposite angles of a parallelogram are equal]
In the triangle:
x
+
∠
P
S
R
+
∠
A
B
C
= 180
∘
[Angle sum property]
⇒
x
= 180
∘
− (70
∘
+ 60
∘
)
⇒
x
=50
∘
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