Exercise 5 Page 400

To find the measure of an exterior angle of a regular pentagon, 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 $36 0^{\circ} .$

This means that the sum of the exterior angles of a regular pentagon is also $36 0^{\circ} .$ A pentagon has $5$ vertices and $5$ exterior angles.

In a regular polygon, all exterior angles are congruent. Therefore, a regular pentagon has

5

congruent exterior angles. To find the measure of one of them, we will divide

36 0^{\circ}

by

5 .

\frac{3 6 0}{5} = 7 2^{\circ}