Each interior angle of a regular R-gon is precisely 59/58 times that of each angle of a regular S-gon, where R ≥ S ≥ 3.

Find the largest possible value of S.

Denote by r and s number of sides of R & S respectively.

Since ((r-2)/r)/((s-2)/s)=59/58 and (s-2 )/s approaches 1

(s-2)/s must be less than 58/59

**58s= 59s-118 yields s=118**

**therefore:**

**117 is the maximal integer value for S.**

there was no requirement to evaluate angles for S and R .but they can be easily derived.

*Edited on ***January 16, 2015, 4:49 am**