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July 24th, 2017, 06:56 PM   #1
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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?
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July 24th, 2017, 07:02 PM   #2
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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 $180 - \dfrac{360}{n}$

$\displaystyle \lim_{n \to \infty} 180 - \dfrac{360}{n}$
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