1. The problem is to find the measure of an exterior angle of a regular hexadecagon, which is a polygon with 16 sides. 2. The sum of the exterior angles of any polygon is always $360^\circ$. 3. For a regular polygon, all exterior angles are equal, so the measure of each exterior angle is given by dividing the total sum by the number of sides. 4. Therefore, the measure of each exterior angle of a regular hexadecagon is $$ \frac{360^\circ}{16} $$. 5. Simplifying, $$ \frac{360}{16} = 22.5^\circ $$. 6. Hence, the measure of each exterior angle of a regular hexadecagon is $22.5^\circ$.