Describing Rotations

Let's begin by drawing a regular hexagon.

If we connect each of the six vertices with the center, we create $6$ congruent angles.

Knowing that a full turn is $360^\circ,$ we can calculate the measure of each angle. $\dfrac{360^\circ}{6}=60^\circ$ Therefore, a $60^\circ$ rotation about the center maps the polygon onto itself.

The same is true if we rotate the polygon $120^\circ$ and $180^\circ$ about the center.

We have found three angles of rotation that map the figure onto itself and they are $60^\circ,$ $120^\circ,$ and $180^\circ.$