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The measure of an exterior angle of a regular 7-sided polygon is 51.4° to the nearest tenth degree

Step-by-step explanation:

In any regular polygon:

  • The length of all sides are equal
  • The measures of all angles are equal
  • 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 its exterior angle at one of its vertices are supplementary

∵ The polygon is regular with 7-sides

∴ n = 7

∵ The measure of an exterior angle = [tex]\frac{360}{n}[/tex]

- Substitute n by 7 in the rule above

∴ The measure of an exterior angle = [tex]\frac{360}{7}[/tex]

∴ The measure of an exterior angle = 51.42857 degrees

- Round it to the nearest tenth degree

∴ The measure of an exterior angle = 51.4° → to the nearest tenth degree

The measure of an exterior angle of a regular 7-sided polygon is 51.4° to the nearest tenth degree

Learn more:

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

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