# Relationship between angles

It turns out there is a relation between angle a and angle b. I can't figure it out, could someone give me a hint?

There's a lightray that is bouncing from two mirrors (m1 and m2).

The angle between those two mirrors is called a.

The angle between the incoming lightray l1 and the mirror m1 is called x.

The angle between the incoming lightray l1 and the outgoing lightray l3 called b.

## 1 Answer

The point is every incoming and reflected angle makes equal angles. $X+K=180^\circ-a$ $b=360^\circ-2(x+k)$ then $b=2a$

• Why is b=360-2(x+k) ? – user108681 Nov 15 '13 at 15:04
• "b" is an external angle of the triangle made by l1,l2, and l3. It equals the sum of two non-adjacent angles which are 180-2x and 180-2k respectively. Hope this helps. – Omid Nov 15 '13 at 17:24