Question

letters x, y, and z are angle measures. which equations would guarantee that lines p and q are parallel? check all that apply. x = z x + y = 180° x + z = 180° x = y z = 180°

Explanation:

Step1: Recall parallel - line angle rules

When two lines are cut by a transversal, alternate - interior angles are equal if the lines are parallel. Here, \(x\) and \(z\) are alternate - interior angles. If \(x = z\), then lines \(p\) and \(q\) are parallel.

Step2: Analyze \(x + y=180^{\circ}\)

\(x\) and \(y\) are not supplementary angles that would guarantee parallel lines. Supplementary angles that guarantee parallel lines are same - side interior angles. Here \(x\) and \(y\) are not in the correct position for this rule.

Step3: Analyze \(x + z = 180^{\circ}\)

\(x\) and \(z\) are alternate - interior angles and they should be equal for parallel lines, not supplementary.

Step4: Analyze \(x = y\)

\(x\) and \(y\) are not corresponding angles or any other angle pair that would guarantee parallel lines with the given relationship.

Step5: Analyze \(z = 180^{\circ}\)

An angle measure of \(180^{\circ}\) for \(z\) does not guarantee that lines \(p\) and \(q\) are parallel.

Answer:

\(x = z\)