The Path of a Billiard Ball

1. A billiard ball starts from one corner of a equilateral triangular pool table. The ball bounces 5 times and returns to the original corner. Find the original angle of travel of the ball. [Let the initial corner be located at the origin and the other corners be (10,0) and (5,5rt3).]
2. Repeat for 7 bounces.
3. For what initial angles will the ball end at the same corner (and how many bounces)?
4. For what initial angles will the ball end at a different corner (and how many bounces)?

Source: Many sources, submitted by Ravi Subramanian.