How many sides does a regular polygon have if the measure of an exterior angle is `24^0?`

Answer

To find 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, each exterior angle can be calculated by dividing this total by the number of sides \(n\).

2. **Set up the equation:**
Since we know that each exterior angle is \(24^\circ\), we can set up the equation:
\[ \text{Exterior angle} = \frac{360^\circ}{n} \]
Substituting the given exterior angle:
\[ 24^\circ = \frac{360^\circ}{n} \]

3. **Rearrange the equation to 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 number of sides of the regular polygon is \(15\).

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