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Your winnings will be added to your other taxable income and will be taxed all together based on your total income, filing status, deductions etc.
Thus if you are single, do not have any other deductions or credits, and $80,000.00 from a sweepstakes - your only taxable income - your estimated 2009 tax liability will be $13,850
Virginia state income tax will be extra - http://www.tax.virginia.gov/web_pdfs/taxtable.pdf
I would estimate ~$3800.
Let me know if you need any help.