A polygon has 44 diagonals. Find the number of its sides

• nC2 - n = 44 (given), then
  
  ½ n (n - 1) - n = 44
  
  n^2 - n - 2 n = 88
  
  n^2 - 3 n - 88 = 0
  
  Solving the quadratic, we have
  
  n^2 - 11 n + 8 n - 88 = 0
  
  (n - 11) (n + 8) = 0
  
  Since, n = -8 is not applicable, hence the polygon in question must have 11 number of sides to it
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