Question

A ray $\text{OA}$ is incident upon a smooth surface $\text{POQ}$. It is reflected back along $\text{OB}$, a normal $\text{ON}$ is drawn perpendicular to the surface at $\text{O}$ (the point of incidence) and the value of $\angle \text{AOP}$ is ${60}^{\circ }$. Find the value of $\text{x}$ in degrees.

• A. 30

Answer 1

The correct option is A 30
$\angle \text{AOP}+\angle \text{AON}={90}^{\circ }$
(as $\text{ON}$ is perpendicular to $\text{POQ}$)
Given, $\angle \text{AOP}={60}^{\circ }$
$⟹\angle \text{AON}={90}^{\circ }-{60}^{\circ }$​
$\angle \text{AON}={30}^{\circ }$

By the laws of reflection,
$\angle \text{AON}=\angle \text{BON}=\text{x}$
Thus, $\text{x}={30}^{\circ }$