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, \((7x - 17)+(7x + 1)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(7x-17 + 7x+1=(7x + 7x)+(-17 + 1)=14x-16\). The equation becomes \(14x-16 = 180\).

Step3: Solve for \(x\)

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

Answer:

\(x = 14\)