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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 = [tex]\frac{(n-2)*180}{n}[/tex] , where n is the number of its sides
  • The measure of each exterior angle = [tex]\frac{360}{n}[/tex]
  • 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 = [tex]\frac{360}{n}[/tex]

∴ The measure of each exterior angle = [tex]\frac{360}{15}[/tex]

∴ 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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