Lines and Angles (Geometry Guide Chapter 4 4th Edition) #3

[neoanarchist66]

There are a few problems that I that require one to setup a system of two equations. I am having trouble figuring out what equations even need to be setup. For example, problem states that x + (x + y) = 320, what is x? (Please note that there is a picture of two parallel lines cut by a transversal and x and y are supplementary angles)

So, the solution says the equations include 2x + y = 320, which is intuitive if you add x to x from the equation given. The second suggested equation is -x - y = =180. Right here is where I am a little confused of why you would pick this and not x + y = 180. Any assistance and advice on how to solve these two equation type problems is greatly appreciated.