Question

su and vx are parallel lines. which angles are supplementary angles? ∠xwy and ∠utw ∠xwy and ∠str ∠xwy and ∠vwt ∠xwy and ∠vwy

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is $180^{\circ}$.

Step2: Analyze the relationship between $\angle XWY$ and $\angle VWT$

Since $\overleftrightarrow{SU}$ and $\overleftrightarrow{VX}$ are parallel lines and $YR$ is a transversal. $\angle XWY$ and $\angle VWT$ form a linear - pair. A linear - pair of angles is supplementary. That is, $\angle XWY+\angle VWT = 180^{\circ}$.

Step3: Analyze other options

• For $\angle XWY$ and $\angle UTW$: They are not in a position to form a sum of $180^{\circ}$ based on the parallel - line and transversal properties.
• For $\angle XWY$ and $\angle STR$: They are not in a position to form a sum of $180^{\circ}$ based on the parallel - line and transversal properties.
• For $\angle XWY$ and $\angle VWY$: $\angle XWY+\angle VWY

eq180^{\circ}$ (they are adjacent angles but not a linear - pair).

Answer:

$\angle XWY$ and $\angle VWT$