How many sides does a regular polygon have if each of the exterior angles measures 30 degrees?There are number of sides

1. Break Down the Problem

To find the number of sides of a regular polygon when given the measure of each exterior angle, we can use the property that the sum of all exterior angles of any polygon is $360$ degrees.

2. Relevant Concepts

The formula for each exterior angle of a regular polygon with $n$ sides can be expressed as: $\text{Exterior angle} = \frac{360^\circ}{n}$

3. Analysis and Detail

Given that the measure of each exterior angle is $30^\circ$:

$30^\circ = \frac{360^\circ}{n}$

We can rearrange this equation to solve for $n$:

$n = \frac{360^\circ}{30^\circ}$

4. Verify and Summarize

Now, we will calculate $n$:

$n = \frac{360}{30} = 12$

This means that the regular polygon has $12$ sides.

Final Answer

The regular polygon has 12 sides.