.A ray of light falls on a plane mirror at an angle of 45?. Through what
angle is it turned on reflection?

Dear Student,
Let AO be the ray of light incident onto the mirror (MM') at an angle 45^o ​​​​​. The ray will be reflected along OB. According to laws of reflection,
angle of incidence, $\angle AON$ = angle of reflection, $\angle BON$ = 45^o 
If the mirror was not there, the ray would have travelled along OA'.

​​​​​​Now,
AOA' is a straight line.
Thus,
$$\begin{gathered} \angle AON+\angle NOB+\angle BOA\text{'}={180}^o \\ {45}^o+{45}^o+\angle BOA\text{'}={180}^o \\ \angle BOA\text{'}={90}^o \end{gathered}$$

The incident ray will be turned by 90^o.

Regards