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