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 relationships

When two lines are parallel, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary.

Step2: Analyze each option

• For $x = z$: $x$ and $z$ are corresponding angles. If corresponding angles are equal, the lines $p$ and $q$ are parallel.
• For $x + y=180^{\circ}$: $x$ and $y$ are same - side interior angles. If same - side interior angles are supplementary, the lines $p$ and $q$ are parallel.
• For $x + z = 180^{\circ}$: There is no parallel - line angle relationship that states this guarantees parallel lines.
• For $x = y$: $x$ and $y$ are not related by any of the standard parallel - line angle relationships in this case.
• For $z = 180^{\circ}$: This is not a valid condition for parallel lines.

Answer:

$x = z$, $x + y=180^{\circ}$