SOLUTION: One interior angle of a convex polygon is 160 degrees. The rest of the interior angles of the polygon are each 112 degrees. How many sides does the polygon have?

Algebra ->  Polygons -> SOLUTION: One interior angle of a convex polygon is 160 degrees. The rest of the interior angles of the polygon are each 112 degrees. How many sides does the polygon have?      Log On


   

Question 1018924: One interior angle of a convex polygon is 160 degrees. The rest of the interior angles of the polygon are each 112 degrees. How many sides does the polygon have?
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
One interior angle of a convex polygon is 160 degrees. The rest of the interior angles of the polygon are each 112 degrees. How many sides does the polygon have?
-------------------------------------------------- 

Your equation is 

160 + (n-1)*112 = (n-2)*180,   or

160 + 112n - 112 = 180n - 360,   or

180n - 112n = 160 - 112 + 360,   or

68n = 408,

n = 408%2F68 = 6.