Question 626627
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
Note:  {{{D = n(n-3)/2}}}
how many diagonals are there in 80 sides? {{{D = 80(80-3)/2}}}
how many sides are there in 152 diagonals?
 {{{152 = n(n-3)/2}}}
   304 = n^2 - 3n
     n^2 - 3n - 304 = 0
{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{n = (3 +- sqrt( 1225))/(2) }}}
 {{{n = (3 +- 35)/(2) }}}
    n = 19   (tossing out negative solution for n)