Angles and Polygons

Question

Find the measure of each interior angle and each exterior angle of a regular 90-gon.

The measure of each interior angle is ____ , and the measure of each exterior angle is ____.

Answer 1

The sum of the exterior angles of any polygon is 360, so each exterior of a regular 90-gon would be 360/90 = 4

The sum of the interior angles of any polygon is (n-2)180, where n is the number of sides, so the sum of the measures of a 90-gon would be 88 * 180. Each interior angle of a regular 90-gon would thus be 88 * 180/90 = 88 * 2 = 176.