Question 1048508
<pre><b>
{{{expr(1/2)n(n - 3)}}}{{{""=""}}}{{{779}}}

Multiply through by 2:

{{{n(n - 3)}}}{{{""=""}}}{{{1558}}}

{{{n^2 - 3n)}}}{{{""=""}}}{{{1558}}}

{{{n^2 - 3n-1558)}}}{{{""=""}}}{{{0}}}

{{{(n-41)(n+38)}}}{{{""=""}}}{{{0}}}

{{{n-41}}}{{{""=""}}}{{{0}}}; {{{n+38}}}{{{""=""}}}{{{0}}}

{{{n}}}{{{""=""}}}{{{41}}};   {{{n}}}{{{""=""}}}{{{-38}}}

A polygon cannot have a negative number of sides, so

n = 41.

Edwin</pre></b>