Question 230636
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The measure of an interior angle in degrees of a regular <i>n</i>-gon is given by the formula:


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


The measure of an exterior angle in degrees of a regular <i>n</i>-gon is given by the formula:


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


If the interior angle is 11 times the exterior angle we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{(n\ -\ 2)180}{n}\ =\ 11\cdot\frac{360}{n}]


Just solve for *[tex \Large n].  Hint:  Multiply both sides by *[tex \Large \frac{n}{180}] as a first step.



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