Question

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

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two given angles \((5x - 11)^{\circ}\) and \((6x - 7)^{\circ}\) are supplementary (linear - pair of angles). So, \((5x-11)+(6x - 7)=180\).

Step2: Combine like - terms

\[

$$\begin{align*} 5x-11 + 6x-7&=180\\ (5x + 6x)+(-11-7)&=180\\ 11x-18&=180 \end{align*}$$

\]

Step3: Isolate the variable term

Add 18 to both sides of the equation: \(11x-18 + 18=180 + 18\), which simplifies to \(11x=198\).

Step4: Solve for \(x\)

Divide both sides by 11: \(x=\frac{198}{11}=18\).

Answer:

\(x = 18\)