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Number of diagonal in a polygon = \frac{n\times (n-3)}{2}, where n is number of sides

Thus, \frac{n\times (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 = 14 & n = -11

Since, the side can’t be negative. So, n = -11 is rejected.

Hence the number of sides of the polygon is 14

**Video Explanation:**

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