Question

given (lparallel mparallel n), find the value of (x). 120° (x^{circ})

Explanation:

Step1: Identify angle - relationship

Since \(l\parallel m\parallel n\), the \(120^{\circ}\) angle and the angle adjacent to \(x^{\circ}\) are corresponding angles. Corresponding angles formed by parallel lines are equal. So the angle adjacent to \(x^{\circ}\) is \(120^{\circ}\).

Step2: Use linear - pair property

The sum of angles in a linear - pair is \(180^{\circ}\). Let the angle adjacent to \(x^{\circ}\) be \(y = 120^{\circ}\). Then \(x + y=180^{\circ}\).

Step3: Solve for \(x\)

Substitute \(y = 120^{\circ}\) into \(x + y=180^{\circ}\), we get \(x=180 - 120\).
\(x = 60^{\circ}\)

Answer:

\(60\)