Question

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

Explanation:

Step1: Use corresponding - angles property

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

Step2: Simplify the left - hand side

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

Step3: Isolate the variable term

Add 7 to both sides of the equation: \(11x-7 + 7=180 + 7\), so \(11x=187\).

Step4: Solve for x

Divide both sides by 11: \(x=\frac{187}{11}\), and \(x = 17\).

Answer:

\(x = 17\)