y = 10 and x = 12
Because we know that 6y and the blank angle next to 13y - 10 are alternate interior angles, and these angles are equal, then the blank angle next to 13y - 10 must equal 6y.
Since 6y and 13y - 10 are next to each other on a 180 degree line, then added together those angles must equal 180 degrees. We can set up an equation to solve:
6y + (13y - 10) = 180
19y - 10 = 180
19y = 190
y = 10
The same applies for the top, 6y and 9x +12 are on a 180 degree line. We can make another equation
6y + (9x + 12) = 180
We know the value of y so we can plug it in and solve for x now
6(10) + 9x + 12 = 180
60 + 12 + 9x = 180
72 + 9x = 180
9x = 108
x = 12
