Question

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

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two given angles \((2x - 11)^{\circ}\) and \((9x+4)^{\circ}\) are same - side interior angles, and same - side interior angles of parallel lines are supplementary. So, \((2x - 11)+(9x + 4)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+9x-11 + 4=180\), which simplifies to \(11x-7 = 180\).

Step3: Solve for \(x\)

Add 7 to both sides of the equation: \(11x-7 + 7=180 + 7\), getting \(11x=187\). Then divide both sides by 11: \(x=\frac{187}{11}=17\).

Answer:

\(x = 17\)