a polygon of n sides has n(n-3)/2 diagonals. how many sides has a polygon with 54 diagonals - Wikitechy https://www.wikitechy.com/interview-questions/tag/a-polygon-of-n-sides-has-nn-3-2-diagonals-how-many-sides-has-a-polygon-with-54-diagonals/ Interview Questions Tue, 07 Sep 2021 05:34:01 +0000 en-US hourly 1 https://wordpress.org/?v=6.9.4 https://www.wikitechy.com/interview-questions/wp-content/uploads/2025/10/cropped-wikitechy-icon-32x32.png a polygon of n sides has n(n-3)/2 diagonals. how many sides has a polygon with 54 diagonals - Wikitechy https://www.wikitechy.com/interview-questions/tag/a-polygon-of-n-sides-has-nn-3-2-diagonals-how-many-sides-has-a-polygon-with-54-diagonals/ 32 32 A polygon has 77 diagonals. Determine the number of sides ? https://www.wikitechy.com/interview-questions/geometry/a-polygon-has-77-diagonals-determine-the-number-of-sides/ https://www.wikitechy.com/interview-questions/geometry/a-polygon-has-77-diagonals-determine-the-number-of-sides/#respond Tue, 17 Aug 2021 15:36:08 +0000 https://www.wikitechy.com/interview-questions/?p=1807

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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