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