Question 240282
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The measure of an interior angle of a regular *[tex \LARGE n]-gon is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{(n\ -\ 2)180}{n}]


The measure of an exterior angle of a regular *[tex \LARGE n]-gon is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{360}{n}]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{(n\ -\ 2)180}{n}\ =\ t\left(\frac{360}{n}\right)]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (n\ -\ 2)180\ =\ t\left(360\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n\ -\ 2\ =\ 2t]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n\ =\ 2t\ +\ 2\ =\ 2(t\ +\ 1)]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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