Question

In the figure given below, lines RS and PQ intersect each other at point O.
$\text{If}\angle POR:\angle ROQ=5:9,$
find $\angle SOQ$.

• A. 80

Answer 1

The correct option is A 80
$\angle POR+\angle ROQ={180}^{\circ }$
(Linear pair of angles)

but, $\angle POR$ : $\angle ROQ$ = 4 : 5 (given)

$\angle POR=\frac{4}{9}\times {180}^{\circ }={80}^{\circ }$

Similarly, $\angle ROQ=\frac{5}{9}\times {180}^{\circ }={100}^{\circ }$

Now, $\angle POS=\angle ROQ={100}^{\circ }$ (Vertically opposite angles)

And, $\angle SOQ=\angle POR={80}^{\circ }$ (Vertically opposite angles)