Question

given m||n, find the value of x. answer attempt 1 out of 3 x =

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the given angles \((4x + 1)^{\circ}\) and \((2x-19)^{\circ}\) are same - side interior angles, and same - side interior angles are supplementary (their sum is \(180^{\circ}\)). So we set up the equation \(4x + 1+2x-19=180\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant 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 of the equation by 6: \(x=\frac{198}{6}=33\).

Answer:

\(33\)