To calculate the measure of each exterior angle of a regular pentagon, we can use the formula:

$\text{Exterior angle of a regular polygon} = \frac{360^\circ}{n}$

Where $n$ is the number of sides of the polygon. In a regular pentagon, $n = 5$.

$\text{Exterior angle of a regular pentagon} = \frac{360^\circ}{5} = 72^\circ$

So, the measure of each exterior angle of a regular pentagon is 72 degrees.

Would you like further details on this solution? Here are five related questions:

1. What is the sum of the exterior angles of any polygon?
2. How do you calculate the interior angle of a regular pentagon?
3. What is the relationship between the exterior and interior angles of a regular polygon?
4. How do you calculate the exterior angles of a polygon with more than five sides?
5. How does the number of sides in a polygon affect the measure of its exterior angles?

Tip: For any regular polygon, the sum of all exterior angles is always $360^\circ$, no matter how many sides it has!