The exterior angle of a regular polygon is 72 determine the number of sides of the regular polygon

The measure of an exterior angle of a regular polygon is given by the formula:

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

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

We are given that the exterior angle is $72^\circ$.

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

Multiply both sides by $n$:

$$72n = 360$$

Divide both sides by 72:

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

The number of sides of the regular polygon is $\text{5}$.