Question

In a parallelogram PQRS, the bisectors of ZP and ZQ meet at O. Find ZPOQ.​

Answer 1

Answer:

Given that:

∠SPO=∠OPQ and ∠RQO=∠OQP.

∠P+∠Q=180∘         [Since PS∥QR]

21(∠P+∠Q)=2180∘

∠OPQ+∠OQP=90∘               ......(1)

Now, 

In △PQO,

∠OPQ+∠OQP+∠POQ=180∘

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

∠O=90∘.