How do you solve this geometry problem

I'm supposed to find the angle of x and the angle of y. There are two intersecting lines kind of like this: X

The top quadrant has x+2y between the top two lines segments, the right one has x-8y between the line segments, and the bottom one has y+106 between the line segments. The goal is two find angle formed in the left one between those line segments.

I've never seen a problem like this in geometry. What's the best way to solve this one?

Thanks

top-angle = x+2y

bottom-angle = y+106

right-angle = x-8y

left-angle = 360-(x+2y +y+106 +x-8y) = right-angle

360-(2x -5y +106) = x-8y

360-106 -2x +5y = x -8y

-2x -x = -8y -5y -254

3x = 13y +254 ..................................... [1]

Also, top-angle = bottom-angle
x+2y = y+106
x = -y+106 ........................................ [2]

From [1] and [2],
3(-y+106) = 13y +254
-3y +318 = 13y +254
-3y-13y = 254-318 = -64
16y = 64, ===> y = 4 ......................... [3]

From [2] and [3],

x = 102
Now, left-angle = right-angle = x -8y

left-angle = 102 -8*4 = 102-32
LEFT-ANGLE = 70 degree >=================< ANSWER

Unless someone is able to figure out exactly what you are talking about, I think you might need to re-post the question with an exact picture of the problem.