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

A. 15

B. 12

C. 17

D. 14

Answer : D. 14

Explanation:

    • 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.

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