Question

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

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), \(x\) and the \(105^{\circ}\) 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 \(x + 105^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(105^{\circ}\) from both sides of the equation: \(x=180^{\circ}- 105^{\circ}\).
\(x = 75^{\circ}\)

Answer:

\(75^{\circ}\)