Final answer:
The value of x that would make lk ∥ om is x = 2.
Step-by-step explanation:
The side-splitter theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides the two sides proportionally. The converse of this theorem states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side. In this case, if lk is parallel to om, the value of x that would make this true is x = 2.
Learn more about side-splitter theorem