# Regular n-gon: Rotation Symmetry

- Author:
- WheelerELHS, GeoGebra Materials Team

In this applet, you will investigate the rotation symmetry of a regular n-gon. Each of the polygons below is regular (equiangular and equilateral) and ONE exterior angle is shown. Move the slider and examine what happens to each regular polygon.

## Recall the following discoveries from our last investigation:

**Equilateral triangles**have rotation symmetries that are multiples of 120° (i.e. 120°, 240°, 360°).

**Squares**have rotation symmetries that are multiples of 90° (i.e. 90°, 180°, 270°, 360°).

**Regular pentagons**have rotation symmetries that are multiples of 72° (i.e. 72°, 144°, 216°, 288°, 360°).

## Based on your observations, conjecture a strategy that can be used to calculate the measure of each "mini-rotation" of a regular polygon.

The measure of ONE "mini-rotation" is _____________ to the measure ONE exterior angle in the regular polygon.

Thus, the following formula is most helpful when determining the rotation symmetries within regular polygons: