jmc

Triangle $AFD$ must have a total angle measure of $180^{\circ }$. We know that the other two angles have measures of $2x$ and $2y$, so angle $AFD$ must have a measure of $180-2x-2y=180-(2x+2y)$ degrees. We now look at quadrilateral $ABCD$, whose interior angle measures must sum to $360^{\circ }$. Therefore, we have that $110^{\circ }+100^{\circ }+3y+3x=360^{\circ }$, so $3x+3y=150^{\circ }$. We want to find $2x+2y$, so we multiply both sides of the equation by $2/3$ to get that $2x+2y=100^{\circ }$. We can now substitute in $100^{\circ }$ for $2x+2y$ to find that the measure of angle $AFD$ is $180-(2x+2y)=180-100=\boxed{80}$ degrees.