Exercise 21 Page 386

Now we will find the measure of each interior angle. A regular $n\text{-gon}$ has $n$ congruent angles. Thus to find the measure of one interior angle of the stop sign, we need to divide the sum of measures of all interior angles, $1080^{\circ },$ by the number of sides, $8.$ The measure of each interior angle of the stop sign is $135^{\circ }.$

Exterior Angle

By the Polygon Exterior Angles Theorem the sum of the measures of the exterior angles of a convex polygon is $360^{\circ }.$ A regular $n\text{-gon}$ has $n$ congruent exterior angles. Thus to find the measure of one exterior angle of the stop sign we will divide the sum of all exterior angles, $360^{\circ },$ by the number of sides, $8.$ The measure of each exterior angle of the stop sign is $45^{\circ }.$