A polygon has 65 diagonals. What is the number of sides of the same polygonal?
If you are given the number of sides of a polygon, how do you get the number of diagonals?
You say that given n sides, the number of vertices will be n and for every diagonal you need to select two of these n vertices. From this, you need to subtract 'n' because this selection includes the cases in which we select adjacent vertices too (which form the n sides, not diagonals).
No of diagonals = nC2 - n = n(n-1)/2 - n = 65
On solving, you get n = 13 (or you can plug the options)
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