3/29A - Rotating A Figure Onto Itself Exploration

How many times did the square map onto itself during the course of the 360 degree rotation?

What is the minimum number of degrees for the square to be mapped onto itself?

How many times did the pentagon map onto itself during the 360 degree rotation?

What is the minimum number of degrees in order for the pentagon to map onto itself?

Using all of the above data, can you produce a formula that would find the minimum number of degrees needed in order for any regular polygon to be mapped onto itself?