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 July 24th, 2017, 05:56 PM #1 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 616 Thanks: 82 What Does The Average Angle Measure Approach? A triangle has an average angle of 60 degrees. A quadrilateral has an average angle of 90 degrees. A figure with 24 sides has an average angle of 165 degrees. As the number of sides approaches infinity, what does the average angle measure approach?
 July 24th, 2017, 06:02 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,770 Thanks: 1424 the sum of the exterior angles of any n-gon will always be 360 degrees, so the average exterior angle will be $\dfrac{360}{n} \implies$ the average interior angle will be $180 - \dfrac{360}{n}$ $\displaystyle \lim_{n \to \infty} 180 - \dfrac{360}{n}$ Thanks from EvanJ

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