## 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

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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2 weeks 2021-11-22T04:01:48+00:00 1 Answer 0

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 = • The measure of each exterior angle = • 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 = – Substitute the measure of the exterior angle by 60 – 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