Now you're thinking with angles!

Wait but you can't just sub x+y with w+z. (Its given, my brain forgot about it)

how do you know that x+y=w+z? isn't that already assuming that they are equal? what if they're one degree off?

But how do you know it's 360? If it wasnt a line, it could be 359.999 Or lets say 350, then w+z is 175.

The 360-ness you take is from the point of view where you already expect it to be a line.