Question 666800
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The measure of an interior angle of a regular *[tex \LARGE n]-gon is given by:


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


The measure of an exterior angle of a regular polygon is given by


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


Given the stated 5 to 1 ratio,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{180(n\ -\ 2)}{n}\ =\ \frac{5(360)}{n}]


Equal fractions with equal denominators must have equal numerators:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 180(n\ -\ 2)\ =\ 5\,\cdot\,360]


Solve for *[tex \LARGE n]   Hint:  Divide through by 180 before you do anything else.


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