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°
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° |
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°.how the interior and exterior angle of a polygon add up to 180°