Question

if an exterior angle of a regular polygon measures 60°, how many sides does the polygon have? sides submit

Explanation:

Step1: Recall the formula for the sum of exterior angles of a regular polygon.

The sum of the exterior angles of any regular polygon is always \(360^\circ\). Let \(n\) be the number of sides of the regular polygon.

Step2: Use the formula for the measure of each exterior angle.

The measure of each exterior angle of a regular polygon is given by \(\frac{360^\circ}{n}\). We know that each exterior angle measures \(60^\circ\), so we can set up the equation \(\frac{360^\circ}{n}=60^\circ\).

Step3: Solve for \(n\).

To solve for \(n\), we can multiply both sides of the equation by \(n\) to get \(360^\circ = 60^\circ\times n\). Then, divide both sides by \(60^\circ\): \(n=\frac{360^\circ}{60^\circ}\).

Step4: Calculate the value of \(n\).

\(\frac{360^\circ}{60^\circ} = 6\).

Answer:

6