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The Sum of an Interior and Exterior Angle of a Polygon Equals 180 Degrees (Mathematics Lesson)

The Sum of an Interior and Exterior Angle of a Polygon Equals 180 Degrees

The sum of an interior and exterior angle in a polygon is 180°:

A Real Example of the Sum of the Interior and Exterior Angle in a Polygon Equals 180°

Question: What is the exterior angle θ of the polygon below?



Step 1: The interior and exterior angle add up to 180°.

100° + θ = 180°.

Step 2: Find θ.

θ = 180° - 100°.

θ = 80°

Another Real Example of the Sum of the Interior and Exterior Angle in a Polygon Equals 180°

Question: What is the interior angle θ of the polygon below?



Step 1: The interior and exterior angle add up to 180°.

θ + 120° = 180°.

Step 2: Find θ.

θ = 180° - 120°.

θ = 60°

Yet Another Real Example of How to Find the Exterior Angle of a Regular Polygon

The slider below shows a real example of the sum of an interior and exterior angle in a polygon equalling 180°:

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Note

FIND THE MISSING ANGLE

The fact that the interior and exterior angle in a polygon add up to 180° allows a missing angle to be found.

Interior Angle + Exterior Angle = 180°

If either of the angles is known, the other can be found.

Use algebra to rearrange this equation:

Interior Angle = 180° - Exterior Angle

Exterior Angle = 180° - Interior Angle

INTERIOR AND EXTERIOR ANGLES AT THE SAME VERTEX ADD UP TO 180°

Only interior and exterior angles at the same vertex (corner) of the polygon add up to 180°.

If they are at a different vertex, there is not necessarily any relationship between them.