Question 676464
First, we must realize the operative word is supplementary. This tells us that the two angles will add up to 180. (Let me preface this by saying that I could solve this algebraically, but it is actually much easier to solve it mentally. If you need me to work it out more in-depth, just shot me an e-mail.) 

The two angles are: 122 and 58. 
122+58=180, so it is supplementary. And, the difference between them is 64. 

Thus, 122 and 58 are your answers.