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?

Step-by-Step:

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°

Answer:

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?

Step-by-Step:

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°

Answer:

The exterior angle is 80°.

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See Also

What is an angle?