the equation d=1/2n (n-3) gives the number of diagonals D for polygon with n sides. use this equation to find the number of sides n for a polygon that has 65 diagonals

To solve this problem you must apply the proccedure shown below:

 1. You have that:

 - The equation d=1/2(n(n-3)) gives the number of diagonals for the polygon.

 - The polygon that has 65 diagonals..

 2. When you clear n, you obtain:

 d=n(n-3)/2
 d=(n^2-3n)/2
 2x65=n^2-3n
 n^2-3n-130=0
 
 3. When you solve the quadratic equation, you obtain:

 n=13

 Therefore, the answer is: 13 sides.