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

## 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°: Don't forget: This interior angle and exterior angle must be at the same vertex (corner) of the polygon for this to be the case.

## How to Find a Missing Angle Using the Sum of the Interior and Exterior Angle in a Polygon Equalling 180°

Because an interior angle and an exterior angle at a vertex sum to 180°, we can find:

• a missing interior angle when the exterior angle is known.

• a missing exterior angle when the interior angle is known.

### Finding a Missing Interior Angle

Finding a missing interior angle is easy.

### Question

What is the interior angle θ of the polygon below? # 1

The interior and exterior angle add up to 180°.

θ + 120° = 180°

# 2

Find θ by subtracting the exterior angle (120°) from 180°

θ = 180° − 120° = 60°

The interior angle is 60°.

### Finding a Missing Exterior Angle

Finding a missing exterior angle is easy.

### Question

What is the exterior angle Φ of the polygon below? # 1

The interior and exterior angle add up to 180°.

100° + Φ = 180°

# 2

Find Φ by subtracting the interior angle (100°) from 180°

Φ = 180° − 100° = 80°