Question

PQRS is a parallelogram. The angle
bisectors of angle P and angles
meet at O. The measure of angle
POS is *
O 60 degree
O 100 degree
O 90 degree
O 45 degree​

Answer 1

Answer:

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Answer 2

Answer:

Given that:

∠SPO=∠OPQ and ∠RQO=∠OQP.

∠P+∠Q=180∘

[Since PS∥QR]

1/2 (∠P+∠Q)= 180∘/2

∠OPQ+∠OQP=90∘ ......(1)

Now,

In △POQ,

∠OPQ+∠OQP+∠POQ=180∘.....[angle sum property of triangle]

90°+∠POQ=180°.....[From equation (1)]

∠POQ=180°-90°

∠POQ=90 ∘

∠POQ+∠POS=180°......[Linear pair]

90°+∠POS=180°

∠POS=180-90°

∠POS=90°

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