Exterior Angle of Regular Polygon

Theorem

Let $P$ be a regular polygon with $n$ sides.

Then each of the exterior angles of $P$ is equal to $\dfrac {360 \degrees} n$.

Proof

From Sum of External Angles of Polygon equals Four Right Angles, the sum of all $n$ exterior angles of $P$ equals $360 \degrees$.

We have a fortiori that the interior angles of $P$ are equal.

Hence the exterior angles of $P$ are also equal.

Hence each exterior angle of $P$ equals $\dfrac {360 \degrees} n$.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polygon
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polygon