Answers

  • Brainly User
2015-11-07T18:09:37+08:00
Answer: Nonagon

Number of Diagonals = n(n-3)
                                       2

n = number of sides
27 = given number of diagonals

27 = n(n-3)
          2

27 = n
² - 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.


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