How to Calculate the Initial Angle of Incidence in a Mirrored Maze?

[mrlucky0]

Homework Statement

In an amusement park maze with all the walls covered with mirrors, Pilar sees Hernando's reflection from a series of three mirrors. If the reflected angle from mirror 3 is 52° for the mirror arrangement shown in the figure, in which = 12°, what is the angle of incidence on mirror 1?

Homework Equations

law of reflection:
angle incident = angle reflected (with respect to normal)

The Attempt at a Solution

Working backwards, I arrived at 40 degrees.

 

[Astronuc]

Angle $\beta$ = 12°?

 

[mrlucky0]

Yes, alpha = 52, beta = 12.

Just hope if anyone can confirm my answer. I worked it through and did not have to use trig.