Understanding and Calculating Exterior Angles of Polygons: A Comprehensive Guide

Exterior Angle

The exterior angle of a polygon is an angle formed by extending one of the sides of the polygon and the adjacent side

The exterior angle of a polygon is an angle formed by extending one of the sides of the polygon and the adjacent side. In other words, it is an angle formed outside the polygon at one of its vertices.

To find the measure of an exterior angle, we can use the fact that the sum of the measures of exterior angles of a polygon is always 360 degrees.

If we have a regular polygon (all sides and angles are equal), we can find the measure of each exterior angle by dividing 360 degrees by the number of sides. For example, in a regular pentagon (a polygon with five sides), each exterior angle will measure 360 degrees divided by 5, which is 72 degrees.

For irregular polygons (sides and angles are not equal), finding the measure of an exterior angle may require more steps. One way is to extend one of the sides to create a straight line, forming a linear pair with the interior angle at that vertex. The exterior angle will be the sum of the measures of the interior angle and its adjacent exterior angle.

For example, let’s say we have a polygon with an interior angle of 80 degrees. To find the measure of its adjacent exterior angle, we subtract 80 degrees from 180 degrees (since they form a linear pair). Thus, the adjacent exterior angle will be 180 degrees – 80 degrees = 100 degrees.

Keep in mind that the exterior angle can also be negative if the interior angle is larger than 180 degrees. For instance, if we have an interior angle of 200 degrees, its adjacent exterior angle would be 180 degrees – 200 degrees = -20 degrees.

It’s important to remember that the exterior angle always lies on the outside of the polygon, while the interior angle lies on the inside. The sum of each exterior angle with its adjacent interior angle is always 180 degrees, forming a straight line.

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