Question

In the figure given below, lines RS and PQ intersect each other at point O.
$\text{If}\angle POR:\angle ROQ=11:13,$
find $\angle SOQ$.

Answer 1

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

but, $\angle POR$ : $\angle ROQ$ = 11 : 13 (given)

$\angle POR=\frac{11}{24}\times {180}^{\circ }=(\frac{165}{2}{)}^{\circ }$

Similarly, $\angle ROQ=\frac{13}{24}\times {180}^{\circ }=(\frac{195}{2}{)}^{\circ }$

Now, $\angle POS=\angle ROQ=(\frac{195}{2}{)}^{\circ }$ (Vertically opposite angles)

And, $\angle SOQ=\angle POR=(\frac{165}{2}{)}^{\circ }$ (Vertically opposite angles)