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First of all its not NANOGON its NONAGON......... A nonagon has 9 sides..
360/9 = 40 degrees
I donno :P
A nanogon has no diagonals because there is no such shape. A nonagon, on the other hand, has 9*(9-3)/2 = 27 diagonals.
Assuming you mean 1,120, because each angle in a nanogon is 140 degrees so the ninth angle is 140 as well. But if this is an irregular nanogon then...it`s still possible to figure out...your last angle would be 130 degrees.