# Find the measure of the central angles of a regular polygon with 12 sides?

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### Can a regular polygon's interior angles measure 40 degrees?

No. To elaborate, the smallest regular polygon, an equilateral triangle, has 60 degree interior angles. The next larger one, a square, has 90 degree interior angles. In fact, for any regular polygon, the interior angles measure 180*(n-2)/n degrees, where n is the number of sides. No polygon has less than 3 sides. Thus, no regular polygon can have interior angles less than 60 degrees.

### Calculate the measure of a central angle of a regular onehundred and eighty-sided polygon?

The sum of the interior angles of a regular polygon is 2n-4 right angles where n is the number of sides. If n = 180, then 2n - 4 = 360 - 4 = 356 right angles. Each interior angle therefore measures 356 x 90 ÷ 180 = 178°. The central angle of each segment of this polygon therefore measures 180 - 178 = 2°.