Question 326196
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Let *[tex \Large n] be the number of sides for this polygon.  The measure of each interior angle of a regular polygon is given by:


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


The measure of each external angle of a regular polygon is given by:


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


We are given that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 14\left(\frac{360}{n}\right)\ =\ \frac{(n\ -\ 2)180}{n}]


Multiply both sides by *[tex \Large n]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 14\,\cdot\,360\ =\ (n\ -\ 2)180]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n\ -\ 2\ =\ 28]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n\ =\ 30]


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