Question

Lines PQ and RS intersect at O. If$\angle POR:\angle ROQ=5:7$. Then $\angle POS$ =

• A. ${105}^{\circ }$
• B. ${75}^{\circ }$
• C. ${45}^{\circ }$

Answer 1

The correct option is A ${105}^{\circ }$


$\angle POR+\angle ROQ={180}^{\circ }$(linear pair) and given $\angle POR:\angle ROQ$ = 5:7

Therefore $\angle POR=\frac{5}{12}\times 180={75}^{\circ }$
and $\angle ROQ=\frac{7}{12}\times 180={105}^{\circ }$

$\angle POS=\angle ROQ$(vertically opposite angles)
$\to \angle POS={105}^{\circ }$