Answer
x=60, y=60
Work Step by Step
The book's method is completely valid. I find, however, that it is sometimes beneficial to see a different way of doing a problem when trying to understand a topic. Thus, I provided an alternative method to solving this problem:
We see that y and the 120 degree angle form a linear pair. (In other words, they are supplementary and add to 180 degrees.)
Thus:
y+120 = 180
y = 60
Using the fact that triangles add to 180 degrees, we find:
60+60+x = 180
x = 60
