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

(KS2, Year 6)

## The Lesson

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°.## Beware

## 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.**Help Us To Improve Mathematics Monster**

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