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?
StepbyStep:
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?
StepbyStep:
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°.