The interior angles of a convex polygon are in arithmetic progression. The smallest angle is 120 degrees and the common difference is 5 degrees. Find the number of sides of the polygon.
+2666 Write as equation:
\(180(s-2) = s({120 + (120+5s) \over 2})\)
By solving, \(\color{brown}\boxed{s = 12}\)
+2666 ***EDIT***
I forgot to write the arithmetic series part correctly. The equation should be:
\(180(s-2) = s{(120 + (120 + 5(s-1)) \over 2}\)
Solving, we find it can be 9, or 16. It can't be 16, because the largest angle is greater than 180, and then it would not be a convex polygon.
Thus, the CORRECT answer is \(\color{brown}\boxed{9}\)
Thank You Geno for telling me!!!
