Question

What is the measure of an exterior angle in a regular polygon with 15 sides?

Answer 1

Answer: 24°

Step-by-step explanation: The formula for finding the measure of each exterior angle of a regular polygon is similar to the formula for finding the measure of each interior angle. All we have to do is take the sum of the measures of the exterior angles which is always 360° divided by the number of sides in the polygon which is n.

$\frac{360}{n}$

Since the polygon has 15 sides, we simply plug a 15 in for n.

$\frac{360}{15}$

360 ÷ 15 = 24

Therefore, the measure of each exterior angle of a regular polygon that has 15 sides is 24°.

Answer 2

First, find the measure of an interior angle:
the sum of the interior angles of a polygon is (n-2)*180, n is the number of sides
for a 15-sided polygon, the sum is 13*180
each interior angle is then 13*180/15=156
the measure of each exterior angle=180-156=24