Question

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

Explanation:

Step1: Find the measure of \(x\)

Since \(x\) and \(125^{\circ}\) are supplementary angles (they form a linear pair), we use the formula \(x + 125^{\circ}=180^{\circ}\).

$$x=180^{\circ}- 125^{\circ}$$

$$x = 55^{\circ}$$

Step2: Find the measure of \(y\)

Because lines \(m\) and \(n\) are parallel, \(x\) and \(y\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(y=x\).

$$y = 55^{\circ}$$

Step3: Find the measure of \(z\)

\(z\) and \(y\) are vertical angles. Vertical angles are equal. So \(z=y\).

$$z = 55^{\circ}$$

Answer:

\(m\angle x = 55^{\circ}\), \(m\angle y=55^{\circ}\), \(m\angle z = 55^{\circ}\)