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.

Guest Mar 11, 2022

#1**+1 **

Write as equation:

\(180(s-2) = s({120 + (120+5s) \over 2})\)

By solving, \(\color{brown}\boxed{s = 12}\)

BuilderBoi Mar 11, 2022

#2**+1 **

***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!!!

BuilderBoi
Mar 11, 2022