Question

given ( m parallel 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 \((9x - 9)+(x - 1)=180\).

Step2: Simplify the equation

Combine like - terms: \(9x+x-9 - 1=180\), which simplifies to \(10x-10 = 180\).

Step3: Solve for \(x\)

Add \(10\) to both sides: \(10x=180 + 10=190\). Then divide both sides by \(10\): \(x=\frac{190}{10}=19\).

Answer:

\(19\)