Question

Find the measure of each exterior angle of a regular 15-gon.

Answer 1

The measure of each exterior angle of a regular 15-side polygon is

24°

Step-by-step explanation:

In any regular polygon

• All sides are equal in lengths
• All angles are equal in measures
• The measure of each interior angle = $\frac{(n-2)*180}{n}$ , where n is the number of its sides
• The measure of each exterior angle = $\frac{360}{n}$
• The interior angle and the exterior angle at any vertex are supplementary

∵ The polygon is regular

∵ It has 15 sides

∴ n = 15

∵ The measure of each exterior angle = $\frac{360}{n}$

∴ The measure of each exterior angle = $\frac{360}{15}$

∴ The measure of each exterior angle = 24°

The measure of each exterior angle of a regular 15-side polygon is

24°

Learn more:

You can learn more about polygons in brainly.com/question/6281564

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