The measure of each exterior angle in a regular pentagon is $72^\circ$.

A regular pentagon is characterized by having all sides and angles equal. To determine the measure of each exterior angle, we can use the formula for the exterior angles of any regular polygon. The sum of the exterior angles for any polygon is always $360^\circ$. Given that a pentagon has five sides, we can calculate the measure of each exterior angle by dividing $360^\circ$ by the number of sides:

This indicates that each exterior angle in a regular pentagon measures $72^\circ$. Exterior angles are defined as the angles formed between one side of the polygon and the extension of an adjacent side. In the case of a regular pentagon, since all sides and angles are congruent, each exterior angle is identical.

Understanding this concept is essential, as it aids in analyzing and solving various geometric problems related to regular polygons. For example, knowing the measure of exterior angles allows us to determine the measure of interior angles, since the interior and exterior angles at each vertex of a polygon are supplementary; they add up to $180^\circ$. Consequently, in a regular pentagon, each interior angle can be calculated as:

This foundational knowledge in geometry can be applied to more complex shapes and problems, enhancing your understanding of polygon properties.