Question

Question 22

In the given figure,$\angle ROS$ is a right angle and $\angle POR$ and $\angle QOS$ are in the ratio 1:5. Then, $\angle QOS$ measures

(a) ${150}^{\circ }$
(b) ${75}^{\circ }$
(c) ${45}^{\circ }$
(d) ${60}^{\circ }$

Answer 1

Since $\angle POR$ and $\angle QOS$ are in the ratio 1:5. Let angles be x and 5x, respectively.
We know that, the sum of angles forming linear pair is ${180}^{\circ }\therefore \angle POR+\angle ROS+\angle QOS={180}^{\circ }\Rightarrow x+{90}^{\circ }+5x=180\Rightarrow 6x={180}^{\circ }-{90}^{\circ }\Rightarrow 6x={90}^{\circ }\Rightarrow x=\frac{{90}^{\circ }}{6}\Rightarrow x={15}^{\circ }\therefore \angle QOS=5x=5\times {15}^{\circ }\Rightarrow \angle QOS={75}^{\circ }$