Question

1. a laser light is pointed at a mirror as shown at right. if ∠x measures 48°, what are the measures of ∠y and ∠z? justify your reasons.

Explanation:

Step1: Recall the law of reflection

The angle of incidence is equal to the angle of reflection. Here, $\angle x$ is the angle of incidence and $\angle z$ is the angle of reflection. So $\angle z=\angle x$.
$\angle z = 48^{\circ}$

Step2: Use the fact that $\angle x+\angle y = 90^{\circ}$

Since the normal to the mirror makes a right - angle with the mirror surface, and $\angle x$ and $\angle y$ are complementary angles.
$\angle y=90^{\circ}-\angle x$
$\angle y = 90^{\circ}- 48^{\circ}=42^{\circ}$

Answer:

$\angle y = 42^{\circ}$, $\angle z = 48^{\circ}$