In a regular polygon each interior angle is 120 greater than each exterior angle. Calculate the number of sides of the polygon. ​

Question

In a regular polygon each interior angle is 120 greater than each exterior angle. Calculate the number of sides of the polygon.
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Delwyn 5 years 2021-08-27T07:57:37+00:00 1 Answers 36 views 0

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  1. Nick
    0
    2021-08-27T07:59:25+00:00
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    Answer:

    12 sides.

    Step-by-step explanation:

    the sum of every pair of interior and exterior angle is always 180 degrees.

    x = exterior angle.

    the interior angle is then x+120.

    so then exterior and interior angle together must be 180.

    x + x + 120 = 180

    2x + 120 = 180

    2x = 60

    x = 30 degrees

    how many sides ?

    the sum of all exterior angles must be 360 degrees.

    all exterior angles are the same (because all the interior angles must be the same due to “regular polygon”).

    so, how many times does 30 fit into 360 ?

    360/30 = 36/3 = 12

    it has 12 corners and also sides.

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