Answer: Choice C) line L is parallel to line M by the converse of the same side interior angle theorem
The same side interior angle theorem says that if two lines are parallel (such as L and M) then the same side interior angles that form are supplementary, meaning they add to 180 degrees.
Flip this in reverse, and you'll get the converse which says that if the same side interior angles add to 180, then the lines must be parallel.
note: if line Q is making things more complicated and confusing, then I suggest covering it up or drawing out the diagram again but leaving out line Q