The Lesson
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 polygonThe 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° |
Beware
What Exterior Angles Are...
The exterior angle is the angle between a side and the extension of the side next to it.
...And What Exterior Angles Are Not
The exterior angle of a polygon is not the angle outside of a polygon, between two sides.
Note
What Is a Polygon?
A polygon is a 2-dimensional shape with straight sides.Interior Angles
Polygons have interior angles as well as exterior angles.
The sum of the interior angles of a polygon is given by the formula:
An Interior and Exterior Angle in a Polygon Add Up to 180°
An interior and exterior angle in a polygon add up to 180°.
Read more about how the interior and exterior angle of a polygon add up to 180°
)