Question 346811
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The interior angle and the corresponding exterior angle of any polygon are a linear pair, hence they are supplementary.  From the 3 to 1 relationship we can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x\ +\ x\ =\ 180]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 45]


Since this is a regular polygon, all of the exterior angles are congruent.  The sum of the exterior angles of any polygon is *[tex \Large 360^\circ], hence for a regular polygon the number of sides is given by:


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


where *[tex \Large x] is the measure of the exterior angle.


Substitute and solve for *[tex \Large n]


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