Question

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

Explanation:

Step1: Use the property of same - side interior angles

Since \(m\parallel n\), the sum of the same - side interior angles \((x - 2)^{\circ}\) and \((x - 14)^{\circ}\) is \(180^{\circ}\). So we have the equation \((x - 2)+(x - 14)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x-2+x - 14=(x+x)+(-2 - 14)=2x-16\). The equation becomes \(2x-16 = 180\).

Step3: Solve for \(x\)

Add \(16\) to both sides of the equation: \(2x-16 + 16=180 + 16\), which gives \(2x=196\). Then divide both sides by \(2\): \(x=\frac{196}{2}=98\).

Answer:

\(x = 98\)