Question

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

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two given angles \((10x - 1)^{\circ}\) and \((4x-1)^{\circ}\) are supplementary (same - side interior angles). So, \((10x - 1)+(4x - 1)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(10x+4x-1 - 1=180\), which simplifies to \(14x-2 = 180\).

Step3: Isolate the variable term

Add 2 to both sides of the equation: \(14x-2 + 2=180 + 2\), resulting in \(14x=182\).

Step4: Solve for x

Divide both sides by 14: \(x=\frac{182}{14}=13\).

Answer:

\(x = 13\)