Question

In the figure below, lines RS and PQ intersect each other at point O. If $\angle POR:\angle ROQ=7:13$ , find $\angle SOQ$.

Answer 1

$\angle$ POR + $\angle$ ROQ = ${180}^{\circ }$ (linear pair of angles)

$\angle$ POR : $\angle$ ROQ = 7:13 (given)

$\angle$ POR = $\frac{7}{20}$ $\times$ ${180}^{\circ }$ = ${63}^{\circ }$

$\angle$ ROQ = $\frac{13}{20}$ $\times$ ${180}^{\circ }$ = ${117}^{\circ }$

Now, $\angle$ POS = $\angle$ ROQ = ${117}^{\circ }$ (vertically opposite angle)

And, $\angle$ SOQ = $\angle$ POR= ${63}^{\circ }$ (vertically opposite angles)