Exterior angles of regular polygons
for 8th grade

Exterior angles of regular polygons

The exterior angle of a polygon is the angle made by one side of the polygon and the extension of the next side of the polygon. By applying the angles on a straight line rule, we know that the interior angle plus the exterior angle sum to 180°. The sum of the exterior angles of polygons is always 360°.

This topic deals with regular polygons. Regular polygons have equal length sides and each of their interior angles is identical. Examples of regular polygons are equilateral triangle, square, regular hexagon, etc. Because their interior angles are identical, their exterior angles are also identical. The formula for calculating the exterior angle of regular polygons is:

Exterior angle = 360° / n

(where 360° = total of exterior angles and n = number of sides)

So, for a regular 3 sided polygon (an equilateral triangle), the exterior angle is:

360° / 3 = 120°

For a regular 4 sided polygon (a square), the exterior angle is:

360° / 4 = 90°

For a regular 5 sided polygon (a regular pentagon), the exterior angle is:

360° / 5 = 72°