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22 May, 20:51

An interior angle of a regular polygon has a measure of 108. What type of polygon is it?

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Answers (2)
  1. 22 May, 20:53
    0
    pentagon
  2. 22 May, 21:10
    0
    pentagon

    Step-by-step explanation:

    Recall that for any regular polygon, the number of sides and the interior angles are related through the following formula.

    Interior Angle, θ = 180 (n-2) / n; where n is the number of sides

    Rearranging:

    θ = 180 (n-2) / n

    nθ = 180 (n-2)

    nθ = 180n - 2 (180)

    nθ = 180n - 360

    180n - nθ = 360

    n (180 - θ) = 360

    n = 360 / (180 - θ) (given that θ = 108°)

    n = 360 / (180 - 108)

    n = 5

    since the polygon has 5 sides, it is a pentagon
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