Question

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

Explanation:

Step1: Recall Supplementary Angles

Supplementary angles sum to \(180^\circ\) (a straight angle).

Step2: Analyze Each Pair

• \(\angle TUW\) and \(\angle VUR\): Vertical angles, equal (not supplementary, unless \(90^\circ\), not implied).
• \(\angle TUW\) and \(\angle QRU\): Corresponding angles (parallel lines, transversal), equal (not supplementary).
• \(\angle TUW\) and \(\angle SRP\): \(\angle SRP\) and \(\angle QRU\) are vertical, \(\angle TUW\) and \(\angle QRU\) equal, so not supplementary.
• \(\angle TUW\) and \(\angle TUR\): \(\angle TUR\) is a straight angle? No, \(\angle TUR\) and \(\angle TUW\) form a linear pair (share a side, form a straight line), so they sum to \(180^\circ\) (supplementary).

Answer:

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