Question

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

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle TUR\) and \(\angle TUW\)

These two angles form a linear pair. A linear pair of angles is supplementary. So, \(\angle TUR+\angle TUW = 180^{\circ}\).

Step3: Analyze \(\angle VUW\) and \(\angle SRU\)

Since \(\overrightarrow{QS}\parallel\overrightarrow{TV}\), \(\angle VUW=\angle SRU\) (corresponding angles). Their sum is not \(180^{\circ}\) unless they are \(90^{\circ}\) each (not indicated in the problem).

Step4: Analyze \(\angle QRU\) and \(\angle VUR\)

Since \(\overrightarrow{QS}\parallel\overrightarrow{TV}\), \(\angle QRU=\angle VUR\) (alternate - interior angles). Their sum is not \(180^{\circ}\) unless they are \(90^{\circ}\) each (not indicated in the problem).

Step5: Analyze \(\angle VUW\) and \(\angle TUR\)

There is no property (such as linear - pair, same - side interior angles etc.) that makes their sum \(180^{\circ}\).

Answer:

\(\angle TUR\) and \(\angle TUW\)