Question 980345
<font face="Times New Roman" size="+2">


Exterior angles are supplementary to the corresponding interior angle so there must be two interior angles that measure 139.  That, together with the fact that there are five 147 degree interior angles means that there are *[tex \Large n\ -\ 7] interior angles that measure 123.5.


Since the sum of the interior angles in any polygon is given by *[tex \Large 180(n\ -\ 2)], solve


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 180(n\ -\ 2)\ =\ (2\cdot 139)\ +\ (5\cdot 147)\ +\ \left(123.5(n\ -\ 7)\right)]


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 \ \ \ \ \ \ \ \ \ \