To determine the exterior angle of a regular polygon, you can use a simple formula: divide $360^\circ$ by the number of sides of the polygon.

A regular polygon is defined as a geometric shape in which all sides and angles are equal. The exterior angle is formed between one side of the polygon and the extension of an adjacent side. An important property of polygons is that the sum of all exterior angles is always $360^\circ$, regardless of the number of sides. This property is crucial for calculating the measure of each exterior angle in a regular polygon.

To find the measure of an exterior angle, you take the total sum of the exterior angles ($360^\circ$) and divide it by the number of sides (or vertices) of the polygon. For example, consider a regular hexagon, which has $6$ sides. To calculate the exterior angle, you would perform the following operation:

Thus, each exterior angle of a regular hexagon measures $60^\circ$.

This method is applicable to any regular polygon, whether it is a triangle ($3$ sides), a square ($4$ sides), a pentagon ($5$ sides), or any other regular shape. The formula can be summarized as follows:

This straightforward calculation enables you to quickly determine the exterior angle, which is beneficial in various geometric problems and proofs.