Let x be sides of polygon.

No. of Diagonals = 27

According to formula,

No. of Diagonals

n (n - 3) = 54

n² – 3n – 54 = 0

(n + 6) (n - 9) = 0

n = -6 or 9

Since, no of sides can’t be negative.

So, No. of sides of polygon will be 9.