Question

A polygon has 54 diagonals. The number of sides of this polygon is

Answer 1

Answer: the polygon's name is dodecagon and it has 12 sides .

Step-by-step explanation:

Answer 2

★Assume number of sides of polygon be n.

$\tt{\rightarrow\dfrac{n(n-1)}{2}-n}$

$\tt{\rightarrow\dfrac{n(n-1)}{2}=n=54}$

n² - n - 2n = 108

n² - 3n - 108 = 0

n² - 12n + 9n - 108 = 0

n(n - 12) + 9(n - 12) =0

★n = 12