Question

given ( m||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, the sum of same - side interior angles is \(180^{\circ}\). So, \((6x - 9)+(2x-19)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(6x+2x-9 - 19=180\), which simplifies to \(8x-28 = 180\).

Step3: Isolate the term with \(x\)

Add \(28\) to both sides of the equation: \(8x-28 + 28=180 + 28\), getting \(8x=208\).

Step4: Solve for \(x\)

Divide both sides by \(8\): \(x=\frac{208}{8}=26\).

Answer:

\(26\)