Question

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

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the \(109^{\circ}\) angle and the angle adjacent to \(x\) are corresponding angles and are equal. Let the angle adjacent to \(x\) be \(y\), so \(y = 109^{\circ}\).

Step2: Use linear - pair property

\(x\) and \(y\) form a linear - pair (a straight - line angle), and the sum of angles in a linear - pair is \(180^{\circ}\). So \(x+ y=180^{\circ}\), then \(x = 180^{\circ}-y\).

Step3: Calculate the value of \(x\)

Substitute \(y = 109^{\circ}\) into the equation \(x = 180^{\circ}-y\), we get \(x=180 - 109=71^{\circ}\).

Answer:

\(71^{\circ}\)