On a month page whose dates have faded, the dates of the five Mondays add up to 80. On which day of the week does that month begin?

Five Mondays are $x,x+7,x+14,x+21,x+28$ with sum $5x+70=80$, so the first Monday is the 2nd. Then the 1st is a Sunday. (Monday would need the first Monday to be the 1st, giving a sum of 75.)