Question

How many sides does a regular polygon have if each exterior angle measures 72 degrees?

Answer 1

I think you are supposed to divide the sum of the interior angles of the polygon (360 degrees) by the exterior angles of the polygon (72 degrees). When you do this: 360 / 72 = 5 sides.

This would be a pentagon.

Answer 2

Answer: 5 sides.

Step-by-step explanation:

We know that the total sum of all exterior angles of a regular polygon = 360°

If each exterior angle measures 72 degrees.

Then the number of sides of the regular polygon

$n=\frac{360^{\circ}}{\text{measure of each exterior angles}}=\frac{360^{\circ}}{72^{\circ}}=5$

Therefore,  the regular polygon has 5 sides if each exterior angle measures 72 degrees.