jmc

Starting from the right triangle that contains angle $C$, we can see the third angle in this triangle is $90-26=64$ degrees. By vertical angles, this makes the rightmost angle in the triangle containing angle $y$ also equal to 64 degrees. Thus, the third angle in that triangle has measure $180-(y+64)=116-y$ degrees. Now, we can turn our attention to the five sided figure that contains angles $A$, $B$, and $x$. By vertical angles the right most angle will be $116-y$ degrees. The angle with exterior measure of $x$ degrees will have an interior measure of $360-x$ degrees. Finally, the sum of the angles in a five sided polygon will be equal to $(5-2)180=540$ degrees. So, we can write $$A+B+360-x+90+116-y=540$$ $$28+74+360-x+90+116-y=540$$ $$\boxed{128}=x+y$$