Question

Determine the degree measure of one angle of a 36-sided regular polygon.

a 170°
b 180°
c 6,120°
d 6,480°

Answer 1

To determine the degree measure of one angle of a regular polygon, divide the sum of the interior angles by the number of sides.

The formula for the sum of the interior angles of a polygon is:

Sum = (n - 2) * 180,

where n is the number of sides.

For a 36-sided regular polygon, the sum of the interior angles is:

Sum = (36 - 2) * 180 = 34 * 180 = 6,120°

Since we want to find the measure of one angle, we divide the sum of the interior angles by the number of sides:

Angle measure = Sum / n = 6,120° / 36 = 170°

Therefore, the degree measure of one angle of a 36-sided regular polygon is 170°. Therefore, the answer is option a) 170°.