In a parallelogram PQRS, the bisectors of angle P and angleQ meet at O. Find angle POQ. ​

Question

In a parallelogram PQRS, the bisectors of angle P and angleQ meet at O. Find angle POQ.

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Camila 5 months 2021-12-10T17:06:12+00:00 1 Answer 0 views 0

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    2021-12-10T17:07:24+00:00

    Step-by-step explanation:

    question acha h mujhe aata h par tumhe ni lagta ki points thode kam h

    ____________________________________________

    Given that:

    ∠SPO=∠OPQ∠SPO=∠OPQ and ∠RQO=∠OQP.∠RQO=∠OQP.

    ∠P+∠Q=180∘∠P+∠Q=180∘         [Since PS∥QRSince PS∥QR]

    12(∠P+∠Q)=180∘212(∠P+∠Q)=180∘2

    ∠OPQ+∠OQP=90∘∠OPQ+∠OQP=90∘               ……(1)

    Now, 

    In △PQO,△PQO,

    ∠OPQ+∠OQP+∠POQ=180∘∠OPQ+∠OQP+∠POQ=180∘

    ∠POQ=90∘∠POQ=90∘                       [From equation (1)]

    ∠O=90∘.∠O=90∘.     

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