Question

The measure of the exterior angle regular polygon is 30 degrees. How many sides does it have?

Answer 1

12 sides.

Explanation:

By the Exterior Angle Formula, the sum of the exterior angles in any polygon is `360°`. Since the polygon is regular, all the angles are congruent. This is very important: if the polygon was not regular, the exterior angles could be `30°, 170°,` and `160°`!

Anyway, we can name the number of sides `s` and the number of angles `a`. Because every polygon has the same number of sides and angles (because they are closed figures with non-intersecting lines), `a=s`. Since all the angles are congruent, `30a=360`, and `a=12`. Since `a=s`, `s=12`, so the polygon has 12 sides. (This polygon has a short name: a dodecagon).