Exterior Angle
The angle between an edge of the polygon and the extension of an adjacent line segment outward from the polygon in the direction of the first edge.
An exterior angle is an angle that is formed outside of a polygon where one of its sides is extended. For example, in the polygon shown below, the red angle is an exterior angle.
The measure of an exterior angle of a polygon is equal to the sum of the measures of its adjacent interior angles. This is known as the Exterior Angle Theorem.
For example, in the polygon above, if we know that angle A and angle B are adjacent interior angles, then the measure of the exterior angle is equal to the sum of those two angles:
Measure of exterior angle = measure of angle A + measure of angle B
If we let x be the measure of angle A and y be the measure of angle B, then we can write the equation as:
Measure of exterior angle = x + y
The Exterior Angle Theorem can be used to find the measure of an unknown angle in a polygon, as long as you know the measures of the adjacent interior angles.
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