Certainly! Let's solve the problem step-by-step.
Step 1: Understand the relationship between exterior angles and sides of a polygon.
- The sum of the exterior angles of any polygon is always 360 degrees.
Step 2: Use the measure of one exterior angle to find the number of sides.
- If we know the measure of one exterior angle, we can determine the number of sides of the polygon using the formula:
[tex]\[
\text{Number of sides} = \frac{360^\circ}{\text{Measure of one exterior angle}}
\][/tex]
Step 3: Substitute the given exterior angle measure into the formula.
- Given the exterior angle measure is 24 degrees, we can substitute this into our formula:
[tex]\[
\text{Number of sides} = \frac{360^\circ}{24^\circ}
\][/tex]
Step 4: Perform the division.
[tex]\[
\text{Number of sides} = 15
\][/tex]
Therefore, the regular polygon has 15 sides.
