Question

Question 14
In the given figure, POQ is a line. If $x={30}^{\circ }then\angle QOR$ is

(a) ${90}^{\circ }$
(b) ${30}^{\circ }$
(c) ${150}^{\circ }$
(d) ${60}^{\circ }$

Answer 1

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