If in a regular polygon the number of diagonals is 54 , then the...

Number of diagonals of an $′n′$ sided polygon is

${}^{n}{C}_{2}- n = 54$

$\dfrac{n\left(n - 1\right)}{1.2} - n = 54$

$\dfrac{{n}^{2} - n}{2} - n = 54$

${n}^{2} - 3n = 108$

${n}^{2} - 3n - 108 = 0$

\left(n - 12\right)\left(n + 9\right) = 0$<br /><br />$n = 12