Question

In the adjoining figure, PQRS is a parallelogram.
PO and QO are the bisectors of angle P and angles Q, respectively. Find angle POQ.​

Answer 1

Given -

$\texttt{PQRS is a ||gm}$

$\texttt{PO and OQ are bisectors of ∠P and ∠Q.}$

To Find -

$\texttt{measure of ∠POQ}$

Solⁿ -

$\texttt{∵ PQRS is a llgm}$

$\mathtt{∴ ∠SPQ + ∠RQP = 180° \;\;\;\;\;\; [adj. \; ∠s \; of \; a \; ||gm]}$

$\texttt{dividing both sides by 2}$

$\mathtt{\frac{∠SPQ}{2} + \frac{∠RQP}{2} = \frac{180°}{2}}$

$\implies \mathtt{∠OPQ + ∠OQP = 90°}$

$\texttt{In ∆OPQ,}$

$\mathtt{∠OPQ + ∠OQP + ∠POQ = 180° \;\;\;\; [∠ \; sum \; prop.]}$

$\implies \mathtt{90°+ ∠POQ = 180°}$

$\implies \mathtt{∠POQ = 90°}$