Question 1186813
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If n is the number of sides of the polygon, then the number of diagonals is<br>
{{{(n(n-3))/2}}}<br>
The given condition is then this:<br>
{{{(n(n-3))/2=10n}}}
{{{(n^2-3n)/2=10n}}}
{{{n^2-3n=20n}}}
{{{n^2-23n=0}}}
{{{n(n-23)=0}}}<br>
n=0 or n=23; obviously n=0 makes no sense, so n=23<br>
The polygon has 23 sides.<br>
For the NAME of that polygon, you can do an internet search....<br>