Final answer:
The measure of an exterior angle of a regular 20-gon is 18 degrees, calculated by dividing 360 degrees by the number of sides of the polygon (360°/20).
Step-by-step explanation:
The measure of an exterior angle of a regular 20-gon can be found using the understanding that the sum of the exterior angles of any polygon is 360 degrees. Since a regular 20-gon has all its exterior angles equal, we simply divide 360 degrees by the number of exterior angles.
The formula used to calculate the measure of an exterior angle (E) of a regular n-gon is:
E = 360° / n
Substitute 20 for n to obtain the measure of an exterior angle of a regular 20-gon:
E = 360° / 20
E = 18°
Therefore, the measure of an exterior angle of a regular 20-gon is 18 degrees.