Question

If $\angle PQRand\angle ROQ$ form a linear pair and they are in ratio of $5:7$. Find $\angle ROQ$~

Answer 1

Given:$\angle POR:\angle ROQ=5:7$

Let $\angle POR=5x$ and $\angle ROQ=7x$

Now, $\angle POR+\angle ROQ={180}^{\circ }$

$\Rightarrow 5x+7x={180}^{\circ }$

$\Rightarrow 12x={180}^{\circ }$

$\Rightarrow x=\frac{{180}^{\circ }}{12}={15}^{\circ }$

$\therefore \angle POR=5x=5\times {15}^{\circ }={75}^{\circ }$ and $\angle ROQ=7x=7\times {15}^{\circ }={105}^{\circ }$

Hence $\angle ROQ=7x=7\times {15}^{\circ }={105}^{\circ }$