In this diagram we see that 80 and 3x+4y are both vertical angles and vertical angles are congruent or always equal so we can set those two equations equal to each other then we can see that a line splits two angles making them supplementary (they equal 180 degrees) So we can have another equation, the two equations are:
3x+4y=80 and 3x+4y+7x-8y=180 (add like terms to simplify and get 10x-4y=180
Then use elimination to get rid of the y variables
10x-4y=180 (plus)
+3x+4y=80 (the negative 4 and positive 4 cancels each other out so you are left with:)
13x=160 (divide by x)
x=12.30769 which can be rounded to x=12.31
Then we have to plug in x into the first equation:
3(12.31) + 4y = 80
36.93 + 4y = 80 (subtract 36.93 from 80)
4y = 43.07 (divide)
y=10.7675 or rounded to 10.77
so x=12.31 and y=10.77