Question

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

Explanation:

Step1: Use the property of parallel lines

When two parallel lines \(m\parallel n\) are cut by a transversal, the sum of the interior angles on the same side of the transversal is \(180^{\circ}\). So, \((7x - 17)+(7x + 1)=180\).

Step2: Simplify the equation

Combine like - terms: \(7x+7x-17 + 1=180\), which simplifies to \(14x-16 = 180\).

Step3: Solve for \(x\)

Add \(16\) to both sides of the equation: \(14x=180 + 16\), so \(14x=196\). Then divide both sides by \(14\): \(x=\frac{196}{14}=14\).

Answer:

\(14\)