The measure of an exterior angle of a regular polygon is given below. Find the measure of an interior angle. Then find the number of sides. 72 What is the measure of an interior angle? T

To find the measure of an interior angle of a regular polygon when given an exterior angle of 72 degrees, first use the fact that the interior angle and exterior angle are supplementary. So, the measure of the interior angle would be 180 - 72 = 108 degrees. To find the number of sides, use the formula for the exterior angle: 360 divided by the number of sides. Therefore, the polygon has 360 / 72 = 5 sides, meaning it's a pentagon! In ancient Greece, mathematicians explored the properties of polygons extensively, leading to the discovery of formulas that are still used today. The study of regular polygons dates back to figures like Euclid, who examined geometric shapes and their relationships, paving the way for modern geometry and concepts of angles. In real-world contexts, regular polygons appear everywhere! From the design of stop signs (which are octagons) to architectural structures like the Pentagon, the principles of polygons help create aesthetically pleasing and structurally sound designs. Understanding the basics of polygons can aid in design and engineering tasks!