Exterior Angle of Regular Polygon
Jump to navigation
Jump to search
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