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

1 Answer
The Legend
Feb 28, 2018

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).

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