Exterior Angles of a Polygon
(KS2, Year 6)

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 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°

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°
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See Also

What is an angle?