Question 1001860
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The measure of an exterior angle of any regular polygon is *[tex \Large \frac{360}{n}]


The measure of an interior angle of any regular polygon is *[tex \Large \frac{(n\ -\ 2)180}{n}]


Since the measure of an interior angle of the polygon under consideration is two times the measure of the exterior angle, we can say that:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{720}{n}\ =\ \frac{(n\ -\ 2)180}{n}]


Solve for *[tex \Large n]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \