Answer: Nonagon
Number of Diagonals = n(n-3)
2
n = number of sides
27 = given number of diagonals
27 = n(n-3)
2
27 = n² - 3n
2
(2) 27 = n² - 3n
54 = n² - 3n
Write as quadratic equation in the form ax² + bx + c = 0
n² - 3n = 54
n² - 3n - 54 =0
Solve by factoring:
(n - 9) (n + 6) = 0
n - 9 = 0 n + 6 = 0
n = 9 n = -6
Choose the possible solution (root), n = 9
The polygon is a nonagon because it has 9 sides.
