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27 May, 15:17

The sum of the measures of the interior angles of a polygon is 500°. what type of polygon is it?

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  1. 27 May, 15:21
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    There is no polygon having interior angles whose measures total 500 degrees.

    Explanation:

    The sum of the interior angles of a polygon with n sides is equal to 180∘ * (n-2).

    So, If there is a polygon whose interior angles total 500 degrees, then

    180∘ * (n-2) = 500

    ∴n-2 = 500∘ 180∘ = 2.78

    ∴n=4.78

    Since n is not a whole number, there is no such polygon whose interior angles total 500 degrees.
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