it depends on what you mean by a diagonal. If you take a diagonal to mean a line from one corner to the "opposite" corner, then a nonagon doesn't have any, and a decagon has five. The reason a nonagon doesn't have any, is that the corners aren't opposite each other.
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There are 35 diagonals in a 10 sided decagon
A tetra-decagon is a 14 sided polygon having 77 diagonals
35
A nonagon has 9 sides whereas a decagon has 10 sides
27