Twice the amount Nigel originally had is 2 * 45 = <<2*45=90>>90 dollars
Now, Nigel has 10 dollars more, meaning that he has 10 + 90 = <<10+90=100>>100 dollars
Before his mother gave him 80 dollars, he had been left with 100 - 80 = <<100-80=20>>20 dollars
This means that Nigel gave away 45 - 20 = <<45-20=25>>25 dollars
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