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 \(t\), consecutive interior angles are supplementary. So \((6x - 1)+(11x - 23)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(6x+11x-1 - 23=180\), which gives \(17x-24 = 180\).

Step3: Solve for \(x\)

Add \(24\) to both sides of the equation: \(17x-24 + 24=180 + 24\), so \(17x=204\). Then divide both sides by \(17\): \(x=\frac{204}{17}=12\).

Answer:

\(12\)