The measure of each exterior angle is 60° and the polygon has 6 sides ⇒ 4th answer
Step-by-step explanation:
In a regular n-side polygon:
∵ The measure of an interior angle of a regular polygon is 120°
∵ The sum of interior angle and exterior angle at a vertex = 180°
∴ The measure of each exterior angle = 180 - 120
∴ The measure of each exterior angle = 60°
∵ The measure of each exterior angle = [tex]\frac{360}{n}[/tex]
- Substitute the measure of the exterior angle by 60
∴ [tex]60=\frac{360}{n}[/tex]
- By using cross multiplication
∴ 60 n = 360
- Divide both sides by 60
∴ n = 6
∴ The polygon has 6 sides
The measure of each exterior angle is 60° and the polygon has 6 sides
Learn more:
You can learn more about polygons in brainly.com/question/6281564
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