Question

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

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle vertical to the given \(50^{\circ}\) angle has the same measure. So \(z = 50^{\circ}\).

Step2: Use corresponding - angle property

Since lines \(m\) and \(n\) are parallel, corresponding angles are equal. Angle \(x\) and the \(50^{\circ}\) angle are corresponding angles, so \(x=50^{\circ}\).

Step3: Use linear - pair property

Angles \(x\) and \(y\) form a linear - pair. A linear - pair of angles is supplementary, i.e., \(x + y=180^{\circ}\). Substitute \(x = 50^{\circ}\) into the equation: \(y=180^{\circ}-x\). Then \(y = 180 - 50=130^{\circ}\).

Answer:

\(x = 50^{\circ}\), \(y = 130^{\circ}\), \(z = 50^{\circ}\)