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

Answer

To find out 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 exterior angles and the number of sides:**
The sum of all exterior angles of any polygon is always \(360^\circ\). For a regular polygon, all exterior angles are equal.

2. **Set up the equation:**
If each exterior angle measures \(24^\circ\), and the polygon has \(n\) sides, then the equation can be set up as:
\[ n \times 24^\circ = 360^\circ \]

3. **Solve for \(n\):**
To find \(n\), we can rearrange the equation:
\[ n = \frac{360^\circ}{24^\circ} \]

4. **Calculate \(n\):**
Now, perform the division:
\[ n = \frac{360}{24} = 15 \]

5. **Conclusion:**
Therefore, the regular polygon has \(15\) sides.

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