ach exterior angle of a regular polygon measures 15°. How many sides does the polygon have?A.15B.8C.24D.10

1. Break Down the Problem

To find the number of sides in a regular polygon given the measure of each exterior angle, we will relate the exterior angle to the number of sides.

2. Relevant Concepts

The formula for the measure of each exterior angle $E$ of a regular polygon with $n$ sides is given by:

$E = \frac{360°}{n}$

3. Analysis and Detail

Given $E = 15°$, we can set up the equation:

$15° = \frac{360°}{n}$

Now, we will solve for $n$:

1. Multiply both sides by $n$:

$15n = 360$

2. Divide both sides by 15:

$n = \frac{360}{15}$

3. Carry out the division:

$n = 24$

4. Verify and Summarize

We found that $n = 24$. To verify, we can substitute $n$ back into the formula for the exterior angle:

$E = \frac{360°}{24} = 15°$

This confirms our calculation is correct.

Final Answer

The polygon has 24 sides. (Option C)