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:

- T he 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.