Let A_1 A_2 A_3 ... A_{10} be a regular polygon. A rotation centered at A_1 with an angle of a takes A_2 to A_{10}. Given that a < 180 degrees, find a, in degrees.

I think the image above (drawn on GeoGebra) summarizes the situation in your problem. I leave it to you to decide which way you rotate (clockwise or counterclockwise) and by what angle. Good luck.