Which polygon has the same number of sides as diagonals?

Which polygon has the same number of sides as diagonals?
  1. Pentagon
  2. Hexagon
  3. Heptagon
  4. Octagon

Solution

Set $\dfrac{n(n-3)}{2} = n \Rightarrow n-3 = 2 \Rightarrow n = 5$. A pentagon has $5$ sides and $5$ diagonals.

Asked in: IMO

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