Find the measure of each exterior angle of a regular 15-gon.
Understand the Problem
The question is asking to calculate the measure of each exterior angle of a regular 15-sided polygon (15-gon). We'll accomplish this by using formula: Exterior Angle = 360 / n, where n= number of sides.
Answer
$24$
Answer for screen readers
$24$
Steps to Solve
- Identify the given information
The polygon is a regular 15-gon, which means it has 15 sides.
- Apply the exterior angle formula
The formula to find the measure of each exterior angle of a regular polygon is: $$ \text{Exterior Angle} = \frac{360}{n} $$ where $n$ is the number of sides.
- Substitute the number of sides
Substitute $n = 15$ into the formula: $$ \text{Exterior Angle} = \frac{360}{15} $$
- Calculate the exterior angle
Divide 360 by 15: $$ \text{Exterior Angle} = 24 $$
$24$
More Information
The measure of each exterior angle of a regular 15-gon is 24 degrees. All regular polygons have exterior angles that add up to 360 degrees.
Tips
A common mistake is using the formula for the interior angles instead of the exterior angles. The formula for interior angles is more complex and not needed for this problem. Also, forgetting that the formula applies only to regular polygons will produce incorrect answers.
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