Answer:
60°
Explanation:
For six full rotations of a polygon or line from a fixed point it would have to be 60°. THis is because assuming that the six rotations will map whatever you are rotating onto itself that is a full 360° rotation total. Divide the total degree of rotation by how many times you need to rotate it and you get 60° (360°/6 rotations=60° rotations each)
I'm not sure if this was what you were asking but hoped this helped