Question

select the correct answer. a regular polygon has an exterior angle measuring 30°. how many sides does the polygon have? a. 8 b. 10 c. 14 d. 12

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 to find the number of sides.

We know that each exterior angle of a regular polygon is \(\frac{360^\circ}{n}\). Given that each exterior angle is \(30^\circ\), we can set up the equation \(\frac{360^\circ}{n}=30^\circ\).
To solve for \(n\), we can multiply both sides of the equation by \(n\) to get \(360^\circ = 30^\circ\times n\). Then, divide both sides by \(30^\circ\): \(n=\frac{360^\circ}{30^\circ}=12\).

Answer:

D. 12