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The Exterior Angles of a Polygon (Mathematics Lesson)

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:

How to Find the Exterior Angle of a Regular Polygon

Question: What is the exterior angle of a regular hexagon?



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

Using the formula.



Each angle in a 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°
Octogon 360° 45°
Nonagon 360° 40°
Decagon 360° 36°
Dodecagon 360° 30°

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Geometry Lessons
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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°

WHAT EXTERIOR ANGLES ARE AND WHAT THEY ARE NOT

The exterior angle is the angle between a side and the extension of the side next to it.



The exterior angle of a polygon is not the angle outside of a polygon, between two sides.