A polygon of n sides has 105 diagonals, then n is equal to

Step-by-step solution

The total number of lines joining any two points of the polygon is given by ^n C₂ So, ^n C₂=105 aligned & n(n-1) 2 =105 & n^2-n=210 & n^2-n-210=0 & n^2-15 n+14 n-210=0 & n(n-15)+14(n-15)=0 & aligned aligned & (n-15)(n+14)=0 & either n-15=0 or n+14=0 & n=15 or -14 & Number of sides cannot be negative & n=15 aligned