1994 AIME Problem 14

A beam of light strikes \overline{BC}\, at point C\, with angle of incidence \alpha=19.94^\circ\, and reflects with an equal angle of reflection as shown. The light beam continues its path, reflecting off line segments \overline{AB}\, and \overline{BC}\, according to the rule: angle of incidence equals angle of reflection. Given that \beta=\alpha/10=1.994^\circ\, and AB=BC,\, determine the number of times the light beam will bounce off the two line segments. Include the first reflection at C\, in your count.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.