Number of sides from exterior angle
for 8th grade

Regular polygon: calculate the number of sides from the exterior angle

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 number of sides of a regular polygon given it's exterior angle is:

Number of sides = 360° / E

(where 360° = total of exterior angles and E = exterior angle of polygon)

So, for a regular polygon with an exterior angle of 120°, the number of sides is:

360° / 120° = 3

For a regular polygon with an exterior angle of 90°, the number of sides is:

360° / 90° = 4

For a regular polygon with an exterior angle of 72°, the number of sides is:

360° / 72° = 5