Geometry Essentials · Superchallenge problem

Two flat mirrors meet along a line and form a $12^\circ$ angle. A light ray travels in a plane perpendicular to that line, parallel to the first mirror, until it strikes the second mirror. Each time it hits a mirror it reflects, with the angle of incidence equal to the angle of reflection. How many reflections does the ray make in all before it travels away from the mirrors for good?