Question

line n intersects lines l and m, forming the angles shown in the diagram. which value of x would prove l || m? (6x + 42)° (18x - 12)°

Explanation:

Step1: Recall parallel - line property

If two lines \(l\) and \(m\) are parallel and intersected by a transversal \(n\), then corresponding angles are equal. Here, the angles \((6x + 42)^{\circ}\) and \((18x-12)^{\circ}\) are corresponding angles. So, we set up the equation \(6x + 42=18x-12\).

Step2: Solve the equation for \(x\)

First, move the \(x\) - terms to one side: \(42 + 12=18x-6x\).
Combining like - terms gives \(54 = 12x\).
Then, divide both sides by 12: \(x=\frac{54}{12}=\frac{9}{2}=4.5\).

Answer:

\(x = 4.5\)