What is the definition of "supplementary" angles? What does the definition say about their angle sums?
What is the definition of "vertical" angles? What does the definition say about their angle measures?
What is the sum of any two angles which "add" to a straight line?
Use the answers to the above questions to set up the necessary equations and solve for x and y. (You haven't posted the actual question -- what you're supposed to do -- yet, so I'll guess that you have to solve for x and y, rather than finding the measures of the angles. But once you have x and y, finding the measures is simple.)
Eliz.