If a polygon had 166 sides it would have 83 diagonals as each diagonal must join two vertices.
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0.5*(402-120) = 740 diagonals
50*(50 - 3)/2 = 1175 diagonals.
A 9-sided polygon, is named 'Nonagon'. The number of diagonals are '9' From any one node, to the centre of the opposite side. Since there are 9 nodes and 9 lines, then there will be 9 diagonals.
Heptagon
The formula is: 0.5*(n2-3n) where n is the number of sides of the polygon. So: 0.5*(81-27) = 27 diagonals