# What is the measure of an exterior angle of a dodecagon?

Dec 6, 2015

Exterior angles of dodecagon measure ${30}^{o}$.

#### Explanation:

Exterior angle of a dodecagon (12-sided regular polygon) is supplementary to its interior angle.

Sum of all interior angles of $N$-sided regular polygon equals to
$\left(N - 2\right) \cdot {180}^{o}$.
Therefore, sum of interior angles of $12$-sided polygon is
$\left(12 - 2\right) \cdot {180}^{o} = {1800}^{o}$

All 12 interior angles of dodecagon are equal, so each is
${1800}^{o} / 12 = {150}^{o}$

A supplementary exterior angle, therefore, equals to
${180}^{o} - {150}^{o} = {30}^{o}$

Dec 6, 2015

30˚
For a regular $n$-gon, the measure of an exterior angle is (360˚)/n.
Since a dodecagon has $12$ sides, an exterior angles is (360˚)/12=30˚.