In a parallelogram PQRS, the bisectors of ∠P and ∠Q meet at O. Find ∠POQ.
Solution:
Given, PQRS is a parallelogram
The bisectors of ∠P and ∠Q meet at O.
We have to find the value of ∠POQ.
Given, OP and OQ are the bisectors of ∠P and ∠Q.
so, ∠OPQ = 1/2 ∠P
∠OQP = 1/2 ∠Q
The opposite sides of a parallelogram are parallel and equal.
Since PS || QR, the consecutive angles are supplementary.
∠P + ∠Q = 180° ------------ (1)
Considering triangle POQ,
By angle sum property of a triangle, the sum of three interior angles of a triangle is equal to 180 degrees.
So, ∠OPQ + ∠POQ + ∠PQO = 180°
1/2 ∠P + ∠POQ + 1/2 ∠Q = 180°
∠POQ = 180° - 1/2 ∠P - 1/2 ∠Q
∠POQ = 180° - 1/2 (∠P + ∠Q)
From (1),
∠POQ = 180° - 1/2 (180°)
∠POQ = 180° - 90°
Therefore, ∠POQ = 90°
✦ Try This: The four angles of a quadrilateral are in the ratio 2 : 3 : 5 : 7. Find the angles.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Solved Problem 30
In a parallelogram PQRS, the bisectors of ∠P and ∠Q meet at O. Find ∠POQ.
Summary:
In a parallelogram PQRS, the bisectors of ∠P and ∠Q meet at O. The value of ∠POQ is 90 degrees.
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