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47 sides.

Take a vertex of an n-sided polygon.

There are n-1 other vertices.

It is already joined to its 2 neighbours, leaving n-3 other vertices not connected to it.

Thus n-3 diagonals can be drawn in from each vertex.

For n=50, n-3 = 50-3 = 47 diagonals can be drawn from each vertex.

The total number of diagonals in an n-sided polygon would imply n-3 diagonals from each of the n vertices giving n(n-3). However, the diagonal from vertex A to C would be counted twice, once for vertex A and again for vertex C, thus there are half this number of diagonals, namely:

number of diagonals in an n-sided polygon = n(n-3)/2.

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