1. We are asked to find the measure of an exterior angle of a regular octagon. 2. A regular octagon has 8 equal sides and 8 equal exterior angles. 3. The sum of all exterior angles of any polygon is always $360$ degrees. 4. Since the octagon is regular, each exterior angle measures $$\frac{360}{8} = 45$$ degrees. 5. Therefore, the measure of each exterior angle of the regular octagon is $45$ degrees.