Question

lines m and n are parallel. find the measures of angles x, y, and z in the figure.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle \(x\) and the \(60^{\circ}\) angle are vertical angles. So \(x = 60^{\circ}\).

Step2: Use corresponding - angle property

Since lines \(m\) and \(n\) are parallel, angle \(y\) and the \(60^{\circ}\) angle are corresponding angles. So \(y=60^{\circ}\).

Step3: Use supplementary - angle property

Angle \(y\) and angle \(z\) are supplementary (a linear - pair). Since \(y = 60^{\circ}\), then \(z=180^{\circ}-y\). So \(z = 180 - 60=120^{\circ}\).

Answer:

\(m\angle x = 60^{\circ}\)
\(m\angle y = 60^{\circ}\)
\(m\angle z = 120^{\circ}\)