Exterior Angles of Polygons

Exterior Angles of a Polygon
The exterior angles of a polygon are the angles formed by extending one side of the polygon at each vertex.

The following diagram shows that the sum of the exterior angles of polygons is 360 degrees. Scroll down the page for more examples and solutions for the exterior angles of polygons.

 

Properties of Exterior Angles of a Polygon

1. Sum of Exterior Angles:
   The sum of the exterior angles of any polygon (one at each vertex) is always 360°, regardless of the number of sides.
   
2. Measure of Each Exterior Angle:
   For a regular polygon (all sides and angles are equal), the measure of each exterior angle is:
   Each Exterior Angle = 360°/n
   where n is the number of sides in the polygon.
   
3. Relationship with Interior Angles:
   At each vertex, the exterior angle and the interior angle are supplementary (they add up to 180°):
   Exterior Angle + Interior Angle = 180°
   

Geometry Worksheets
Exterior Angle Worksheet
Printable & Online Geometry Worksheets

Exterior Angles of a Polygon
In a polygon, an exterior angle is formed by a side and an extension of an adjacent side. Exterior angles of a polygon have several unique properties. The sum of exterior angles in a polygon is always equal to 360 degrees. Therefore, for all equiangular polygons, the measure of one exterior angle is equal to 360 divided by the number of sides in the polygon.

Find the Measure of an Exterior Angle of a Regular Polygon

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Exterior angle of a regular polygon
Students learn the definition of a regular polygon, as well as the following formulas related to regular polygons. The measure of each exterior angle of a regular polygon is 360/n degrees.

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Given the exterior angle of a regular polygon, determine the number of sides

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