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



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

    n2 - 3n = 154

    n2 - 3n - 154 = 0

    n2 - 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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