Question

which angles are alternate exterior angles? ∠mnq and ∠pqn ∠pqs and ∠rqs ∠pqs and ∠mnl ∠onl and ∠pqs

Explanation:

Step1: Recall the definition of alternate exterior angles

Alternate exterior angles are non - adjacent angles that lie outside two lines and on opposite sides of a transversal.

Step2: Analyze each pair of angles

• For \(\angle MNQ\) and \(\angle PQN\): These angles are adjacent, so they are not alternate exterior angles.
• For \(\angle PQS\) and \(\angle RQS\): These angles are adjacent (they form a linear pair), so they are not alternate exterior angles.
• For \(\angle PQS\) and \(\angle MNL\): \(\angle MNL\) is not in a position to be an alternate exterior angle with \(\angle PQS\) as per the definition.
• For \(\angle ONL\) and \(\angle PQS\): \(\angle ONL\) and \(\angle PQS\) are non - adjacent, lie outside the lines \(PR\) and \(MO\) and on opposite sides of the transversal \(SL\). So, they are alternate exterior angles.

Answer:

\(\angle ONL\) and \(\angle PQS\)