Question

qs and tv are parallel lines. which angles are supplementary angles? ∠tur and ∠sru ∠tur and ∠vuw ∠tur and ∠qrp ∠tur and ∠tuw

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180 degrees.

Step2: Analyze angle - pairs formed by parallel lines

When two parallel lines ($\overleftrightarrow{QS}$ and $\overleftrightarrow{TV}$) are cut by a transversal ($\overleftrightarrow{WP}$), we use angle - relationships.
For $\angle TUR$ and $\angle SRU$, they are same - side interior angles. Same - side interior angles formed by two parallel lines and a transversal are supplementary. That is, $\angle TUR+\angle SRU = 180^{\circ}$.
For $\angle TUR$ and $\angle VUW$, they are vertical angles and vertical angles are equal, not supplementary.
For $\angle TUR$ and $\angle QRP$, $\angle QRP$ and $\angle SRU$ are vertical angles. $\angle TUR$ and $\angle QRP$ are not supplementary.
For $\angle TUR$ and $\angle TUW$, $\angle TUR+\angle TUW<180^{\circ}$ and they are part of the angles at point $U$.

Answer:

$\angle TUR$ and $\angle SRU$