Question

if a light ray strikes a flat mirror at an angle of 61 degrees above the mirrors surface, what is the angle of reflection in relation to the normal

Answer 1

The Laws of Reflection state that: The angle of incidence = The angle of reflection.
So if by flat mirror, you mean a plane mirror, then if angle of incidence = 52, then the angle of reflection will also be 52.

Answer 2

For any plane reflector, the angle of reflection is always equal to the angle of incidence.

We know that thelight ray at an angle of 61 degrees from above (i assume that those 61° are between the light ray and the surface of the mirror), so the angle with respect to the normal of the mirror will be the complementary angle A = 90° - 61° = 29°

This means that the incidence angle is equal to 29°, then, the reflection angle is also 29°.

Now, if the initial angle is with respect to the normal of the mirror, the reflection angle is equal to it, so the reflection angle is also 61°