If the exterior angle of a regular polygon measures 30°, how many sides does it have?

1. Break Down the Problem

To find the number of sides $n$ of a regular polygon when given the measure of an exterior angle, we can use the relationship between the exterior angle and the number of sides.

2. Relevant Concepts

The formula for the exterior angle $E$ of a regular polygon is given by: $E = \frac{360^\circ}{n}$ Where:

• $E$ is the exterior angle.
• $n$ is the number of sides of the polygon.

3. Analysis and Detail

Given that the exterior angle measures $30^\circ$, we set up the equation: $30^\circ = \frac{360^\circ}{n}$ To find $n$, we can rearrange the formula:

Multiplying both sides by $n$: $30^\circ n = 360^\circ$

Now, dividing both sides by $30^\circ$: $n = \frac{360^\circ}{30^\circ} = 12$

4. Verify and Summarize

We can verify our result by calculating the exterior angle for a polygon with 12 sides: $E = \frac{360^\circ}{12} = 30^\circ$ This confirms that the calculation is correct.

Final Answer

The polygon has 12 sides.