SOLUTION: How many sides does a polygon have if each of its interior angles measure 140? I have tried isolationg for n using the formular (n-2)x180/2.

Algebra ->  Polygons -> SOLUTION: How many sides does a polygon have if each of its interior angles measure 140? I have tried isolationg for n using the formular (n-2)x180/2.      Log On


   

Question 880955: How many sides does a polygon have if each of its interior angles measure 140?
I have tried isolationg for n using the formular (n-2)x180/2.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

I like exterior angles.
Each exterior angle is the supplement of the adjacent interior angle.
If each interior angle measures 140%5Eo ,
then each exterior angle measures 180%5Eo%2B140%5Eo=40%5Eo
The exterior angle is the change in direction as you "turn the corner" at a vertex when going around the perimeter of the polygon.
Then, of course, the sum of all the exterior angles is 360%5Eo ,
because as you finish going around the polygon you have gone one whole turn and are headed in the same direction as when you started.
So if this polygon has n vertices and n sides,
n%2840%5Eo%29=360%5Eo--->n=360%5Eo%2F40%5Eo--->highlight%28n=9%29

THE ALTERNATE, LONGER WAY:
If you want to use the fact that in a polygon with n sides (and n interior angles) the sum of the measures of all those n interior angles is
%28n-2%29%2A180%5Eo ,
knowing that each interior angle measures 140%5Eo ,
you will have to write the equation
%28n-2%29%2A180%5Eo=n%2A140%5Eo .
Solving:
%28n-2%29%2A180%5Eo=n%2A140%5Eo
n%2A180%5Eo-2%2A180%5Eo=n%2A140%5Eo
n%2A180%5Eo-360%5Eo=n%2A140%5Eo
n%2A180%5Eo-n%2A140%5Eo=360%5Eo
n%2A%28180%5Eo-140%5Eo%29=360%5Eo
n%2A40%5Eo=360%5Eo
n=360%5Eo%2F40%5Eo
n=9