Exercise 5 Page 401

To find the measure of an exterior angle of a regular decagon, we will first recall an important piece of information.

Exterior Angles of a Polygon

In a polygon, the sum of the measures of the exterior angles — one at each vertex — is $360^{\circ }.$

This means that the sum of the exterior angles of a regular decagon is also $360^{\circ }.$ A decagon has $10$ vertices and $10$ exterior angles.

In a regular polygon, all exterior angles are congruent. Therefore, a regular decagon has $10$ congruent exterior angles. To find the measure of one of them, we will divide $360^{\circ }$ by $10.$