Lines and Angles — MATHS STD 7 — Question

 It is given that, $POQ$ is a line. Since, sum of all the angles on a straight line is $180^\circ .$
Therefore, $\text{x}+2\text{y}+3\text{y}=180^\circ$
$\Rightarrow\text{x}+5\text{y}=180^\circ$ $[\because\text{x}=30^\circ,\text{given}]$
$\Rightarrow 30^\circ+5\text{y}=180^\circ$
$\Rightarrow 5\text{y}=180^\circ-30^\circ$
$\Rightarrow 5\text{y}=150^\circ$
$\Rightarrow\text{y} = \frac{150^{\circ}}{5}$$$
$\Rightarrow \text{y}=30^\circ$
$\therefore\angle\text{QOR}=3\text{y}=3\times30^\circ=90^\circ$