ACT Math Question?

Question

For all n≥3, let S(n) be the number of diagonals of a polygon with n sides. Anita thinks S(n)=n²-5n+6. Is she correct? Why or why not?

Answer 1

Good job, Anita! You are very close with your answer.

However, the right answer is the following: d = n(n-3)/2.

In this equation, d represents the number of diagonals and n represents the number of sides.

For example, a one can see that a pentagon has five diagonals. When plugging in 5 for n (as a pentagon has 5 sides), we get 5x2/2, resulting in the answer 5 as well.