None. By definition a diagonal goes from one vertex to another vertex and so each diagonal MUST have two vertices.
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3
four (4)
4.
There are 5 diagonals
3. You cannot have a diagonal from a vertex to itself, nor to either of the two adjacent vertices (these would form sides of the polygon). So 3 out of the other vertices cannot be used. In a hexagon, that leaves 3 that can be used. Hence the answer.