If a convex polygon has 170 diagonals. Find the number of sides of the – InterviewSolution

1.

If a convex polygon has 170 diagonals. Find the number of sides of the polygon.

Answer»

Number of diagonals = ⁿC₂ – n = 170.

\(\frac{n(n - 1)}{2} - n = 170\)

n² – n – 2n = 340

⇒ x² – 3x – 340

(n + 17) = 0

n = 20 or -17

∵ n can’t be negative n = 20

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