Split the year 1775 + 16th july 1776

Till 1600 years no odd days.

1601 to 1700 = 5 odd days

1701 to 1775 = 75 + 18 = 93 = 2 odd days. (75 years has 93 odd days (=> 18 leap + 57 non leap years)

upto 15th july 1776 = 31 + 29 + 31 + 30 + 31 + 30 + 15 = 197 = 1 odd day.

Total odd days = 5 + 2 + 1 = 8 = 1 odd day.

So one day after Monday. That is Tuesday.