Question

given m||n, find the value of x.

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), \(x\) and the \(125^{\circ}\) angle are supplementary angles (linear - pair of angles formed by a transversal intersecting two parallel lines).

Step2: Set up equation

The sum of supplementary angles is \(180^{\circ}\), so \(x + 125^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(125^{\circ}\) from both sides of the equation: \(x=180^{\circ}- 125^{\circ}\).
\(x = 55^{\circ}\)

Answer:

\(55\)