Question

given m||n, find the value of x.

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the angles \((5x + 2)^{\circ}\) and \((x - 2)^{\circ}\) are supplementary (same - side interior angles). So, \((5x+2)+(x - 2)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(5x+2+x - 2=6x\). So the equation becomes \(6x = 180\).

Step3: Solve for \(x\)

Divide both sides of the equation \(6x = 180\) by 6. We get \(x=\frac{180}{6}=30\).

Answer:

\(x = 30\)