Each interior angle of a regular n-sided polygon is 150 degrees. How many sides does the polygon have?

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17-07-2014
Mathematics

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Each interior angle of a regular n-sided polygon is 150 degrees. How many sides does the polygon have?

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AL2006 AL2006 · Answer 1 · 2014-07-17T23:12:22+02:00

AL2006 AL2006

17-07-2014

The sum of the interior angles of the polygon = (n - 2) x 180 .

(n - 2) x 180 = (n x 150)

180n - 360 = 150n

Add 360 to each side:

180n = 150n + 360

Subtract 150n from each side:

30n = 360

Divide each side by 30 :

n = 12

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