Exterior Angle of Regular Polygon

From ProofWiki
Jump to navigation Jump to search


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

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


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 $\dfrac {360 \degrees} n$.