How many sides does a regular polygon have if the measure of an exterior angle is `24^@`?

Options

A. `15`
B. `16`
C. `17`
D. `18`

Explanation

To determine how many sides a regular polygon has when the measure of an exterior angle is \(24^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between the exterior angle and the number of sides**:
The formula to find the number of sides \(n\) of a regular polygon based on the measure of an exterior angle \(E\) is given by:
\[ n = \frac{360^\circ}{E} \]

2. **Substitute the given value of the exterior angle**:
We know that the exterior angle \(E\) is \(24^\circ\). So we can substitute this value into the formula:
\[ n = \frac{360^\circ}{24^\circ} \]

3. **Perform the division**:
Now, we will divide \(360\) by \(24\):
\[ n = 15 \]

4. **Conclusion**:
Therefore, the number of sides of the regular polygon is \(15\).

### Final Answer:
The regular polygon has **15 sides**.