SOLUTION: If one of the interior angles of a polygon is 260° and the remaining interior angles are each 160°,find the number of sides of the polygon.

Algebra ->  Polygons -> SOLUTION: If one of the interior angles of a polygon is 260° and the remaining interior angles are each 160°,find the number of sides of the polygon.       Log On


   

Question 824774: If one of the interior angles of a polygon is 260° and the remaining interior angles are each 160°,find 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 in the polygon
The sum of the measures of all interior angles is
%28n-2%29%2A180%5Eo .
So if one interior angle measures 260%5Eo ,
and the n-1 remaining interior angles measure 160%5Eo each,
for the sum of all measures in degrees we can write the equation
260%2B%28n-1%29%2A160=%28n-2%29%2A180

Solving:
%28n-2%29%2A180=260%2B%28n-1%29%2A160
180n-360=260%2B160n-160
180n-160n=260-160%2B360
20n=460
n=460%2F20
highlight%28n=23%29