SOLUTION: Calculate the number of sides a regular polygon has if an interior angle is five times the size of an exterior angle.

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Question 936376: Calculate the number of sides a regular polygon has if an interior angle is five times the size of an exterior angle.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Suppose the interior angle is x degrees.
Then the exterior angle is 180+-+x degrees.

x+=+5%2A%28180-x%29
x+=+900+-+5x
6x+=+900
+x+=+150 degrees.
So exterior angle = 30 degrees.
If the polygon has n sides (and n angles) the sum of its exterior angles is 30%2An
But the exterior angles of a polygon add to 360+ degrees
So, 30%2An+=+360 => n+=+12.
ANSWER: the polygon has 12 sides.