Question

mo and pr are parallel lines. which angles are vertical angles? ∠pqs and ∠onq ∠rqn and ∠onl ∠rqn and ∠pqs ∠mnl and ∠pqn

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are formed when two lines intersect. They are opposite each other and are equal in measure.

Step2: Analyze each option

• For \(\angle PQS\) and \(\angle ONQ\): These angles are not formed by the intersection of the same two lines.
• For \(\angle RQN\) and \(\angle ONL\): These angles are not formed by the intersection of the same two lines.
• For \(\angle RQN\) and \(\angle PQS\): These angles are not formed by the intersection of the same two lines.
• For \(\angle MNL\) and \(\angle PQN\): Lines \(SL\) and \(PR\) intersect at \(Q\), and lines \(SL\) and \(MO\) intersect at \(N\). But when considering the intersection of lines (in terms of vertical - angle formation), \(\angle MNL\) and \(\angle PQN\) are formed by the intersection of two lines (the concept of vertical angles is about two - line intersection). In fact, \(\angle RQN\) and \(\angle PQS\) are not vertical angles. The correct pair is \(\angle RQN\) and \(\angle PQS\) is wrong. The correct analysis: When two lines intersect, for example, if we consider the intersection of a transversal with the parallel lines (but vertical angles are about two - line intersection). The pair \(\angle RQN\) and \(\angle PQS\) are not vertical angles. The pair \(\angle MNL\) and \(\angle PQN\) are vertical angles because they are opposite each other at the intersection of two lines (the lines that form them).

Answer:

\(\angle MNL\) and \(\angle PQN\)