# 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°:##### Curriculum

##### Interactive Test

**show**

##### 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.