Question

given ( mparallel n ), find the value of ( x ).

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), consecutive interior angles are supplementary. That is, \((4x + 2)+(2x-2)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((4x+2x)+(2 - 2)=180\), which simplifies to \(6x=180\).

Step3: Solve for \(x\)

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

Answer:

\(30\)