Question

$\overleftrightarrow{qs}$ and $\overleftrightarrow{tv}$ are parallel lines.
which angles are supplementary angles?
$\angle vuw$ and $\angle tur$
$\angle vuw$ and $\angle sru$
$\angle vuw$ and $\angle tuw$
$\angle vuw$ and $\angle qrp$

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze $\angle VUW$ and $\angle TUW$

Since $\overrightarrow{TV}$ is a straight line, $\angle VUW+\angle TUW = 180^{\circ}$ (they form a linear - pair).

Step3: Analyze $\angle VUW$ and $\angle TUR$

$\angle VUW$ and $\angle TUR$ are vertical angles. Vertical angles are equal, but their sum is not $180^{\circ}$ (unless each is $90^{\circ}$ which is not indicated here).

Step4: Analyze $\angle VUW$ and $\angle SRU$

Since $\overrightarrow{QS}\parallel\overrightarrow{TV}$, $\angle VUW=\angle SRU$ (alternate - interior angles). Their sum is not $180^{\circ}$ (unless each is $90^{\circ}$ which is not indicated here).

Step5: Analyze $\angle VUW$ and $\angle QRP$

$\angle QRP$ and $\angle SRU$ are vertical angles, so $\angle QRP = \angle SRU$. And since $\angle VUW=\angle SRU$ (alternate - interior angles), $\angle VUW=\angle QRP$. Their sum is not $180^{\circ}$ (unless each is $90^{\circ}$ which is not indicated here).

Answer:

$\angle VUW$ and $\angle TUW$