Final answer:
The measure of an exterior angle of a regular 36-gon is 10 degrees, which is calculated by dividing 360 degrees by the number of sides, which is 36.
Step-by-step explanation:
The measure of an exterior angle of a regular 36-gon can be found using the knowledge that the sum of the exterior angles of any polygon is 360 degrees. A regular 36-gon implies that all its sides and angles are equal, therefore each exterior angle would be the total sum of the exterior angles divided by the number of sides. We calculate it as:
Measure of an exterior angle = 360° / 36
Measure of an exterior angle = 10°