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

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

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    2021-11-22T04:03:23+00:00

    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

    #LearnwithBrainly

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