Find the measure of each interior angle AND each exterior angles of the following regular polygons. Show your work.

a. Pentagon

b. 16-gon

c. Dodecagon

Given

regular polygons with 5, 16, and 12 sides

Find

the measures of each interior and exterior angle

Solution

The sum of exterior angles is 360° for any convex polygon. For a regular n-agon, the measure of an exterior angle is 360°/n. The corresponding interior angle is its supplement.

(a) pentagon. Exterior angle: 72°; Interior angle: 108°.

(b) 16-gon. Exterior angle: 22.5°; Interior angle: 157.5°.

(c) dodecagon. Exterior angle: 30°; Interior angle: 150°.