jmc

There are 7 days in a week. Two days of the year fall on the same day of the week if and only if they are congruent modulo 7. Notice that $$284\equiv 4(\mathrm{mod}7)$$ and $$25\equiv 4(\mathrm{mod}7).$$ Therefore the 284th day and the 25th day fall on the same day of the week. Therefore the 284th day of the year falls on a $\boxed{\text{Saturday}}$.