Question

In a parallelogram PQRS, the

bisectors of ∠P and ∠Q meet at
O. Find ∠POQ.​

Answer 1

QUESTION :-

$\sf\red{In \:a \:parallelogram\: PQRS, the\: bisectors \:of \:}$

$\sf\green{∠P \:and \:∠Q \:meet \:at \:O \:Find \:∠POQ.}$

SOLUTION :-

$\rightarrow$ $\sf\pink{Since\: OP \:and \:OQ \:\:are \:the</p><p>\: bisectors}$

$\sf\orange{ \:of \:∠P\: and \:∠Q</p><p> \:respectively,\:}$

$\sf\pink{(see\: figure. ),}$

$\sf\red{So, \:∠OPQ = 1/2\: ∠P\: and \: ∠OQP = </p><p>1/2 \: ∠Q}$

$\sf\purple{ in \:triangle \:POQ}$

$\sf\green{=\:∠OPQ \:+ ∠PQO\: + \:∠POQ = 180°\:(Angle\: sum\: property)}$

$\sf\blue{=\: i.e \:1/2*∠P\:+ \:∠POQ\:+1/2*\:∠Q=180°}$

$\sf\red{ =\:i.e \: ∠POQ =180° -1/2(∠P+∠Q)}$

$\rightarrow$ $\sf\purple{\:180° - 1/2 × 180°}$

$\rightarrow$ $\sf\pink{90°}$

$\rightarrow$ $\sf{\underline{\underline{\blue{\boxed{ ∠POQ\: is \:equal \:to \:90°.}}}}}$