Question

which angles are alternate interior angles?
∠qru and ∠vur
∠qru and ∠tur
∠qru and ∠sru
∠qru and ∠tuw

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent interior angles that lie on opposite sides of the transversal.

Step2: Analyze each pair

• For \(\angle QRU\) and \(\angle VUR\):
• The transversal is \(WU\) (assuming \(WU\) is the line cutting the parallel lines \(QS\) and \(TV\)).
• \(\angle QRU\) and \(\angle VUR\) are non - adjacent interior angles on opposite sides of the transversal \(WU\).
• For \(\angle QRU\) and \(\angle TUR\):
• These angles are adjacent, so they are not alternate interior angles.
• For \(\angle QRU\) and \(\angle SRU\):
• These angles are adjacent (they form a linear pair), so they are not alternate interior angles.
• For \(\angle QRU\) and \(\angle TUW\):
• \(\angle TUW\) is an exterior angle (not an interior angle with respect to the parallel lines \(QS\) and \(TV\) and the transversal), so they are not alternate interior angles.

Answer:

\(\angle QRU\) and \(\angle VUR\)