Question

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

Explanation:

Step1: Use property of parallel lines

When two parallel lines \(m\) and \(n\) are cut by a transversal, the corresponding - angles are equal. Here, the two angles \((3x + 4)^{\circ}\) and \((x - 4)^{\circ}\) are supplementary (since they form a linear - pair along the transversal). So, \((3x + 4)+(x - 4)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x+4+x - 4=3x+x+(4 - 4)=4x\). So the equation becomes \(4x = 180\).

Step3: Solve for \(x\)

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

Answer:

\(45\)