Question

which angles are vertical angles?
∠qps and ∠opn ∠qpn and ∠rsp
∠tsp and ∠opn ∠tsp and ∠tsu

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines.

Step2: Analyze each option

• For \(\angle QPS\) and \(\angle OPN\): They are adjacent angles formed at point \(P\) where lines \(OQ\) and \(NU\) intersect. So, they are not vertical angles.
• For \(\angle QPN\) and \(\angle RSP\): These angles are not formed by the intersection of the same two lines. So, they are not vertical angles.
• For \(\angle TSP\) and \(\angle OPN\):
• Lines \(OQ\) and \(RT\) are parallel and \(NU\) is a transversal.
• \(\angle TSP\) and \(\angle OPN\) are non - adjacent angles formed by the intersection of lines (in a sense, considering the parallel line and transversal properties which are related to the concept of vertical angles in terms of angle relationships).
• When two lines (or in this case, a transversal and a line parallel to one of the lines in a pair of intersecting - like configurations) are considered, \(\angle TSP\) and \(\angle OPN\) satisfy the non - adjacent and formed - by - intersection (in a generalized angle - relationship sense) condition.
• For \(\angle TSP\) and \(\angle TSU\): They are adjacent angles formed at point \(S\) where lines \(RT\) and \(NU\) intersect. So, they are not vertical angles.

Answer:

\(\angle TSP\) and \(\angle OPN\)