How do you find the exterior angle of a regular polygon?

To find the exterior angle of a regular polygon, divide 360 degrees by the number of sides.

A regular polygon is a shape with all sides and angles equal. The exterior angle is the angle formed between one side of the polygon and the extension of an adjacent side. For any polygon, the sum of all exterior angles is always 360 degrees, regardless of the number of sides. This is a key property that helps us find the measure of each exterior angle in a regular polygon.

To calculate the exterior angle, you simply take the total sum of the exterior angles (360 degrees) and divide it by the number of sides (or vertices) of the polygon. For example, if you have a regular hexagon (which has 6 sides), you would calculate the exterior angle by dividing 360 degrees by 6, giving you 60 degrees for each exterior angle.

This method works for any regular polygon, whether it’s a triangle (3 sides), a square (4 sides), a pentagon (5 sides), or any other regular shape. Just remember, the formula is: Exterior Angle = 360° / Number of Sides. This straightforward calculation helps you quickly determine the exterior angle, which is useful in various geometric problems and proofs.