Question

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

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), the sum of same - side interior angles is \(180^{\circ}\). So, \((9x + 4)+(2x-11)=180\).

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for \(x\)

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

Answer:

\(x = 17\)