A polygon has 77 diagonals. Determine the number of sides ?

• The formula for the number of diagonals that can be formed in a polygon with n sides is…..

• n(n – 3)/2 = D, where n = number of sides, D = total number of diagonals in the polygon.

• n(n – 3)/2 = 77

• • n

  2

•  – 3n = 154

• • n

  2

•  – 3n – 154 = 0

• • n

  2

•  – 14n – 11n – 154 = 0

• n(n – 14) + 11(n – 14) = 0

• (n – 14) (n + 11) = 0

n = -11, 14

Reject n=-11 and Accept n=14. Therefore, The number so sides of the polygon is 14.