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July 24th, 2017, 05:56 PM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 651 Thanks: 86  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: 2,981 Thanks: 1575 
the sum of the exterior angles of any ngon will always be 360 degrees, so the average exterior angle will be $\dfrac{360}{n} \implies$ the average interior angle will be $180  \dfrac{360}{n}$ $\displaystyle \lim_{n \to \infty} 180  \dfrac{360}{n}$ 

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angle, approach, average, measure 
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