Answer:
[tex]\angle ABC=20^{\circ}[/tex]
Step-by-step explanation:
Since each side of a line is 180 degrees, we can write the following system of equations:
[tex]\begin{cases}2x+12y+x+2y=180,\\x+2y+8y-4x=180\end{cases},\\\begin{cases}3x+14y=180,\\-3x+10y=180\end{cases}[/tex]
Add both equations to solve for [tex]y[/tex]:
[tex]24y=360,\\y=\frac{360}{24}=15[/tex]
Now substitute [tex]y=15[/tex] into [tex]3x+14y=180[/tex] to solve for [tex]x[/tex]:
[tex]3x+14(15)=180,\\3x=-30,\\x=-10[/tex]
Finish by substituting both variables to solve for [tex]\angle ABC[/tex]:
[tex]\angle ABC=x+2y,\\\angle ABC=-10+2(15),\\\angle ABC=-10+30=\boxed{20^{\circ}}[/tex]
