Question

es The measure of an interior angle of a regular polygon is 120°. What is the measurb of each exterior angle? The polygon has
how many sides?
30 degrees; 6 sides
45 degrees; 8 sides
45 degrees; 6 sides
60 degrees; 6 sides
60 degrees; 8 sides
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Answer 1

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:

• All sides are equal in lengths
• All angles are equal in measure
• The measure of each interior angle = $\frac{(n-2)*180}{n}$
• The measure of each exterior angle = $\frac{360}{n}$
• The sum of interior angle and exterior angle at a vertex is 180°

∵ 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 = $\frac{360}{n}$

- Substitute the measure of the exterior angle by 60

∴ $60=\frac{360}{n}$

- 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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