Question

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

Answer 1

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