Regular n-gon: Rotation Symmetry

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.

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

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