SOLUTION: A polygon has three of its interior angles to be 160 each and others are 120 each. calculate the number of sides of the polygon

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Question 972910: A polygon has three of its interior angles to be 160 each and others are 120 each. calculate the number of sides of the polygon
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
n= number of sides of the polygon ---> n= number of angles of the polygon
3= number of angles of the polygon measuring 160%5Eo
n-3= number of angles of the polygon measuring 120%5Eo
3%28160%5Eo%29%2B%28n-3%29%28120%5Eo%29= sum of the measures of all the interior angles of the polygon.
Since the sum of the measures of all the interior angles of a polygon with n sides is
%28n-2%29%28180%5Eo%29 ,
%28n-2%29%28180%5Eo%29=3%28160%5Eo%29%2B%28n-3%29%28120%5Eo%29
All we have to do no is solve for n the equation above.
Writing it without the degree symbols, it is
180%28n-2%29=3%2A160%2B120%28n-3%29
180%28n-2%29=480%2B120%28n-3%29
180n-360=480%2B120n-360
180n=120n%2B480
180n-120n-480
60n=480
n=480%2F60
highlight%28n=8%29
It is an octagon, and it could look like this:
, but there are other possible shapes.