2.2.5 Exterior/Interior Angles

When finding the exterior, interior, or the sum of exterior or interior angles of a regular n-gon, you can use the following formulas:

Property	Formula
Sum of Exterior Angles	$360^\circ$
Exterior Angle	$\frac{360^\circ}{n}$
Interior Angle	$180^\circ - \frac{360^\circ}{n} = \frac{180^\circ(n - 2)}{n}$
Sum of Interior Angles	$180^\circ(n - 2)$

If you were to only remember one of the above formulas, let it be that the sum of the exterior angles of every regular polygon be equal to 360. From there you can derive the rest relatively swiftly.

Example: Find the sum of the interior angles of an octagon. $P = 180(8 - 2) = 180(6) = 1080^\circ$

Complement and Supplement

In order to find the interior angle from the exterior angle, you used the fact that they are supplements.

• Complement of $\theta$ = $90^\circ - \theta$
• Supplement of $\theta$ = $180^\circ - \theta$

Problem Set 2.2.5