Question

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

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle VUR\) and \(\angle VUW\)

\(\angle VUR\) and \(\angle VUW\) form a linear pair. By the linear - pair postulate, if two angles form a linear pair, then they are supplementary. So \(\angle VUR+\angle VUW = 180^{\circ}\).

Step3: Analyze \(\angle VUR\) and \(\angle SRP\)

Since \(\overleftrightarrow{QS}\parallel\overleftrightarrow{TV}\), \(\angle SRP=\angle VUR\) (corresponding angles). \(\angle VUR+\angle SRP = 2\angle VUR
eq180^{\circ}\) (unless \(\angle VUR = 90^{\circ}\), but there is no information to suggest that).

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

\(\angle TUW=\angle VUR\) (vertical angles). \(\angle VUR+\angle TUW=2\angle VUR
eq 180^{\circ}\) (unless \(\angle VUR = 90^{\circ}\), but there is no information to suggest that).

Step5: Analyze \(\angle VUR\) and \(\angle QRU\)

Since \(\overleftrightarrow{QS}\parallel\overleftrightarrow{TV}\), \(\angle QRU=\angle VUR\) (alternate interior angles). \(\angle VUR+\angle QRU = 2\angle VUR
eq180^{\circ}\) (unless \(\angle VUR=90^{\circ}\), but there is no information to suggest that).

Answer:

\(\angle VUR\) and \(\angle VUW\)