# Definition:Polygon/External Angle

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## Contents

## Definition

Contrary to intuition, the **external angle** of a vertex of a polygon is *not* the size of the angle between the sides forming that vertex, as measured outside the polygon.

An **external angle** is in fact an angle formed by one side of a polygon and a line produced from an adjacent side.

While $\angle AFE$ is the internal angle of vertex $F$, the **external angle** of this vertex is $\angle EFG$.

## Also known as

An **external angle** is also known as an **exterior angle**.

## Also see

- Vertical Angle Theorem, which shows that it does not matter which adjacent side you use, because they are equal.

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**polygon**