Answer:
[tex]x=17[/tex]
Step-by-step explanation:
The two angles labelled [tex]6x+8[/tex] and [tex]4x+2[/tex] are co-interior angles. When two parallel lines are cut by a traversal, co-interior angles are supplementary, meaning they add up to 180 degrees. Therefore, if line L is parallel to line M, [tex]6x+8[/tex] and [tex]4x+2[/tex] must be supplementary:
[tex]6x+8+4x+2=180[/tex]
Combine like terms:
[tex]10x+10=180[/tex]
Subtract 10 from both sides:
[tex]10x=170[/tex]
Divide both sides by 10:
[tex]x=\frac{170}{10}=\boxed{17}[/tex]
