Question

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

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the given angles are same - side interior angles. Same - side interior angles are supplementary, so \((4x + 1)+(2x-19)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(4x+2x + 1-19=180\), which simplifies to \(6x-18 = 180\).

Step3: Isolate the variable term

Add 18 to both sides of the equation: \(6x-18 + 18=180 + 18\), resulting in \(6x=198\).

Step4: Solve for \(x\)

Divide both sides by 6: \(x=\frac{198}{6}=33\).

Answer:

\(x = 33\)