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3 years ago

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

Mathematics

2 answers:

yarga [219]3 years ago

6 0

Answer:

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

sveta [45]3 years ago

4 0

Answer:

pentagon

Step-by-step explanation:

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