Question

Question 147
In parallelogram PQRS, O is the mid-point of SQ. Find $\angle S,\angle R$, PQ, QR and diagonal PR.

Answer 1

Given, $\angle RQY={60}^{\circ }$
$\angle SRQ=\angle RQY$ [$SR\parallel PY$, RQ is the transversal]
$\Rightarrow \angle R={60}^{\circ }$
$\therefore \angle S={180}^{\circ }-\angle R={180}^{\circ }-{60}^{\circ }={120}^{\circ }$ [$\because$ adjacent angles are supplementary]

Also, SR = 15 cm
$\Rightarrow$ PQ = 15 cm [$\because$ opposite sides of a parallelogram are equal]
And PS = 11 cm
$\Rightarrow$ QR = 11 cm [$\because$ opposite sides of a parallelogram are equal]
PR is bisected by SQ, so $PR=2\times PO=2\times 6=12cm$