Question

$overleftrightarrow{rt}$ and $overleftrightarrow{uw}$ are parallel lines.
which angles are supplementary angles?
$angle wvs$ and $angle rsv$
$angle uvs$ and $angle tsv$
$angle tsv$ and $angle tsq$
$angle uvs$ and $angle wvx$

Explanation:

Step1: Define supplementary angles

Supplementary angles sum to $180^\circ$.

Step2: Analyze each option

• $\angle WVS$ and $\angle RSV$: These are alternate interior angles (parallel lines, transversal), so they are equal, not supplementary.
• $\angle UVS$ and $\angle TSV$: These are consecutive interior angles (parallel lines $\overleftrightarrow{RT} \parallel \overleftrightarrow{UW}$, transversal $\overleftrightarrow{XQ}$). Consecutive interior angles are supplementary.
• $\angle TSV$ and $\angle TSQ$: These are adjacent angles forming a ray, not a straight line, so they do not sum to $180^\circ$.
• $\angle UVS$ and $\angle WVX$: These are vertical angles, so they are equal, not supplementary.

Answer:

$\angle UVS$ and $\angle TSV$