SOLUTION: What is the number of sides of a regular polygon if one angle measures 156°

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Question 461249: What is the number of sides of a regular polygon if one angle measures 156°
Found 2 solutions by MathLover1, Gogonati:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Every polygon has interior angles adding up to 180%28n-2%29. In this polygon, the interior angles add up to 156n, where n is the number of sides.
180%28n-2%29=156n
180n+-360+-156n+=0
24n+=+360
n=+15 ........the number of sides of a regular polygon

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the interior angles of a regular polygon with n angles is
%28n-2%29180. Since the angle of our polygon measure 156 degree, then the sum
of interior angles is: n%2A156. Equalizing these two expressions for the sum
of interior angles we have:%28n-2%29%2A180=n%2A156, solving this equation we get:
180n-156n=360 => 24n=360 => n=15.
Answer:The number of sides of our polygon are 15.