Exterior Angle Calculation for Regular Polygons

The sum of the exterior angles of any convex polygon is always $360^{\circ}$.

For a regular polygon, all exterior angles are equal. If a regular polygon has $n$ sides, the measure of each exterior angle is calculated by dividing the total sum of exterior angles ($360^{\circ}$) by the number of sides ($n$).

Formula Used

Exterior Angle = $\frac{360^{\circ}}{n}$

Calculation Steps

• Identify the number of sides ($n$) for the regular polygon. In this case, $n = 15$.
• Substitute the value of $n$ into the formula:

Exterior Angle = $\frac{360^{\circ}}{15}$

• Perform the division:

Exterior Angle = $24^{\circ}$

Therefore, the exterior angle of a regular 15-sided polygon is $24^{\circ}$.