The formula to find the measure of one exterior angle of a regular polygon is:

$\text{Exterior Angle} = \frac{360^\circ}{n}$

where $n$ is the number of sides of the polygon.

Given that the exterior angle is 72°, we can set up the equation:

$72^\circ = \frac{360^\circ}{n}$

To solve for $n$, multiply both sides of the equation by $n$ and divide both sides by 72°:

$n = \frac{360^\circ}{72^\circ} = 5$

Thus, the polygon has 5 sides, meaning it is a regular pentagon.

Summary:

The polygon with an exterior angle of 72° has 5 sides.

Would you like more details, or do you have any other questions? Here are 5 related questions you can explore:

1. What is the sum of the interior angles of a regular pentagon?
2. How do you find the interior angle of a regular polygon?
3. What is the relationship between exterior and interior angles in polygons?
4. What would the exterior angle be for a regular hexagon?
5. Can a polygon have an exterior angle greater than 90°?

Tip: The sum of all exterior angles of any polygon always equals 360°, no matter the number of sides.