SOLUTION: The interior angles of a polygon are in Arithmetic Progression. The smallest angle is 52 degrees and the common difference is 8 degrees. Find the number of sides of the polygon.

Algebra ->  Sequences-and-series -> SOLUTION: The interior angles of a polygon are in Arithmetic Progression. The smallest angle is 52 degrees and the common difference is 8 degrees. Find the number of sides of the polygon.      Log On


   

Question 242977: The interior angles of a polygon are in Arithmetic Progression. The smallest angle is 52 degrees and the common difference is 8 degrees. Find the number of sides of the polygon.
Answer by stanbon(75887) About Me  (Show Source):
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The interior angles of a polygon are in Arithmetic Progression. The smallest angle is 52 degrees and the common difference is 8 degrees. Find the number of sides of the polygon.
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If the smallest interior angle is 52
its corresponding exterior angle is 180-52 = 128 degrees
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As the interior angles increase by 8 degrees
the corresponding exterior angles decrease by 8 degrees.
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Fact: The sum of the exterior angles is 360 degrees
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Equation:
128+ 128-8 + 128-2*8 = 360
There are 3 exterior angles
So the polygon has three sides.
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Cheers,
Stan H.