Question

given ( mparallel n ), find the value of ( x ).

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal, consecutive interior angles are supplementary. So \((9x + 4)+(2x-11)=180\)

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for \(x\)

Add \(7\) to both sides: \(11x=180 + 7\), so \(11x=187\)
Divide both sides by \(11\): \(x=\frac{187}{11}\)

Answer:

\(x = 17\)