Question

find the number of sides of a regular polygon with each exterior angle measuring 6°

Explanation:

Step1: Recall the formula for the measure of an exterior angle of a regular polygon

The formula for the measure of an exterior angle of a regular polygon is \( \text{Exterior angle}=\frac{360^{\circ}}{n}\), where \(n\) is the number of sides.

Step2: Solve for \(n\)

Given that the exterior angle is \(6^{\circ}\), we substitute into the formula: \(6^{\circ}=\frac{360^{\circ}}{n}\).
Cross - multiply to get \(6n = 360\).
Then divide both sides by 6: \(n=\frac{360}{6}\).

Answer:

\(60\)