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740

The number of digaonals is given by n(n-3)/2, where n is the number of sides (or vertices) of a polygon:

40(40-3)/2=20*37=740

For a proof, see:

http://www.artofproblemsolving.com/Wiki/index.php/Diagonal

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Q: How many diagonals will a 40 sided polygon have?
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