Question

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

Answer 1

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
`(N-2)*180^o`.
Therefore, sum of interior angles of `12`-sided polygon is
`(12-2)*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`

Answer 2

`30˚`

Explanation:

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˚`.