Question

solve for x.

Explanation:

Step1: Identify angle - relationship

Assume lines \(LM\) and \(NO\) are parallel. Then, the angles \((5x - 30)^{\circ}\) and \((3x)^{\circ}\) are corresponding angles (or alternate - interior angles depending on the parallel - line properties), and they are equal. So, we set up the equation \(5x-30 = 3x\).

Step2: Solve the equation

Subtract \(3x\) from both sides: \(5x-3x - 30=3x - 3x\), which simplifies to \(2x-30 = 0\). Then add 30 to both sides: \(2x-30 + 30=0 + 30\), getting \(2x=30\). Divide both sides by 2: \(\frac{2x}{2}=\frac{30}{2}\).

Answer:

\(x = 15\)