Question

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

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal, the same - side interior angles are supplementary. So \((x - 4)+(3x + 4)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x-4 + 3x+4=180\), which simplifies to \(4x=180\).

Step3: Solve for \(x\)

Divide both sides of the equation \(4x = 180\) by \(4\), we get \(x=\frac{180}{4}=45\).

Answer:

\(45\)