What is the Angle ϕ of the Reflected Laser Beam in Plane Mirror Reflection?

[Kalibasa]

Homework Statement

A laser beam is incident on the left mirror in the figure below, in which α = 85°. Its initial direction is parallel to a line that bisects the mirrors. What is the angle ϕ of the reflected laser beam?

http://www.webassign.net/knight/p23-40.gif"

Homework Equations

The law of reflection, where the angle of incidence (measured from the normal, the line perpendicular to the surface) is equal to the angle of reflection

The Attempt at a Solution

I tried assigning names to all the angles and figuring out which were equal to each other, then trying to do it algebraically. But I don't see any way to do this with only the one angle given...

 

[collinsmark]

Here's a helpful hint: Regardless of the shape of a given triangle, the sum of its three angles is always 180^o.

Beyond that, if you want us to help more you'll have to show us your work so far, and your attempt at a solution (i.e. show us how you tried to "do it algebraically," for example).

 

[Kalibasa]

How I tried to do it algebraically was a long complicated mess, which is why I didn't post it. I finally figured it out, though- my starting angle was 42.5 degrees, that's what I'd missed, and then I was able to calculate each angle as I went around