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
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