If in a regular polygon, the number of diagonals are 54 , then the number of sides of the polygon are

Step-by-step solution

Number of diagonals in a polygon of n sides is ^ n C ₂- n . aligned & ^ n C ₂- n =54 & n ( n -1) 2 - n =54 & n ^2-3 n -108=0 & ( n -12)( n +9)=0 aligned But, number of sides cannot be negative. n =12