Lego Motor for cycling a tool
It would be difficult to get the exact rotations that you are talking about using Power Functions parts. The servo motor would be your best option, but its range is fixed to +/- 90 degrees from center. If you use a controller with variable speed, it will rotate through 7 steps to get to 90 degrees in either direction.

If you're willing to look at Mindstorms, there is a servo motor with a built-in rotation sensor that was released with both NXT and EV3. These can both be rotated to and from any position, and they are accurate within 1 degree. It sounds like that's the best option to meet your needs.