The Exterior Angles of a Polygon

The Exterior Angles of a Polygon

The exterior angles of a polygon are the angles outside of the polygon, between a side and the extension of the side next to it.

The Sum of the Exterior Angles of a Polygon

The sum of the exterior angles of a polygon is:

The exterior angles of a polygon add up to 360°, a full revolution.

The Exterior Angles of a Regular Polygon

Regular polygons have equal exterior angles.

There are as many exterior angles as there are sides.

To find each exterior angle in a regular polygon, divide the sum of the exterior angles by the number of sides.

The formula for each of the exterior angles of a regular polygon is:

Example

Imagine you wanted to find an interior angle of a regular hexagon.

A regular hexagon has 6 sides, so n = 6.

Using the formula:

Exterior angle = 360° ÷ n

Exterior angle = 360° ÷ 6

Exterior angle = 60°

Each angle in a regular hexagon is 60°.

Read more about how to find the exterior angle of a regular polygon

The Exterior Angles of Different Polygons

Shape Sum of Exterior Angles Exterior Angle of Regular Polygon

Triangle

360° 120°

Quadrilateral

360° 90°

Pentagon

360° 72°

Hexagon

360° 60°

Heptagon

360° 51.4°

Octagon

360° 45°

Nonagon

360° 40°

Decagon

360° 36°

Dodecagon

360° 30°

See Also

What is an angle?