Question

if a regular polygon has interior angles three times the measure of each exterior angle measure, how many sides are there?

Answer 1

Let's assume that our regular polygon has "n" sides.

Each exterior angle of a regular polygon measures 360 degrees divided by the number of sides. Therefore, the measure of each exterior angle is 360/n degrees.

According to the given information, the interior angle is three times the measure of the exterior angle. Thus, the measure of each interior angle is 3 * (360/n) degrees.

In a regular polygon, the sum of all interior angles is equal to (n - 2) * 180 degrees. Therefore, we have:

(n - 2) * 180 = n * (3 * (360/n))

Simplifying the equation:

180n - 360 = 1080

180n = 1440

n = 8

Hence, the regular polygon has 8 sides.