Question

np and qs are parallel lines.
which angles are supplementary angles?
∠qrt and ∠qro ∠nom and ∠por
∠sro and ∠nor ∠nor and ∠pom

Explanation:

Supplementary angles sum to \(180^\circ\). Let's analyze each option:

• \(\angle QRT\) and \(\angle QRO\): These are adjacent angles forming a linear pair? Wait, no—\(\angle QRT\) and \(\angle QRO\) share a common side and vertex, but \(\angle QRT\) is a straight - line - related angle? Wait, actually, \(\angle QRT\) and \(\angle QRO\): \(\angle QRT\) is a straight angle? No, let's re - examine. Wait, \(\angle QRT\) and \(\angle QRO\): \(\angle QRO\) and \(\angle QRT\) – if we look at the line \(QS\) and transversal \(MT\), \(\angle QRO\) and \(\angle SRT\) are supplementary, but \(\angle QRT\) is a straight angle? Wait, no, maybe I made a mistake. Wait, the first option: \(\angle QRT\) and \(\angle QRO\) – actually, \(\angle QRO\) and \(\angle QRT\): \(\angle QRO\) is an angle at \(R\) between \(QR\) and \(RO\), and \(\angle QRT\) is a straight angle? No, maybe not. Let's check the fourth option: \(\angle NOR\) and \(\angle POM\). Wait, \(\angle NOR\): \(NP\parallel QS\), and \(MT\) is a transversal. \(\angle NOR\) and \(\angle SRO\) – no. Wait, the first option: \(\angle QRT\) and \(\angle QRO\). Wait, \(\angle QRO\) and \(\angle QRT\): since \(QR\) is a straight line? No, \(QS\) is a straight line. Wait, \(R\) is on \(QS\), so \(\angle QRO\) and \(\angle SRT\) are supplementary, but \(\angle QRT\) – wait, \(\angle QRT\) is a straight angle? No, maybe the first option: \(\angle QRT\) and \(\angle QRO\) – actually, \(\angle QRO\) and \(\angle QRT\) form a linear pair? Wait, no, \(RO\) and \(RT\) are a straight line? Wait, \(MT\) is a straight line, so at point \(R\), \(\angle QRO\) and \(\angle SRT\) are supplementary, but \(\angle QRT\) – maybe I messed up. Wait, let's recall: supplementary angles add to \(180^\circ\). The first option: \(\angle QRT\) and \(\angle QRO\). Since \(MT\) is a straight line, \(\angle QRO+\angle QRT = 180^\circ\)? Wait, no, \(QR\) is a horizontal line, \(MT\) is a transversal. Wait, \(\angle QRO\) is between \(QR\) and \(RO\), and \(\angle QRT\) is between \(QR\) and \(RT\). Since \(RO\) and \(RT\) are a straight line (because \(MT\) is a straight line), \(\angle QRO+\angle QRT=180^\circ\), so they are supplementary. Wait, but let's check other options:
• \(\angle NOM\) and \(\angle POR\): these are vertical angles, so they are equal, not supplementary (unless they are \(90^\circ\), but we don't know).
• \(\angle SRO\) and \(\angle NOR\): \(NP\parallel QS\), so \(\angle SRO\) and \(\angle NOR\) are alternate interior angles, so they are equal, not supplementary.
• \(\angle NOR\) and \(\angle POM\): these are vertical angles (or related), equal, not supplementary.

So the correct pair is \(\angle QRT\) and \(\angle QRO\).

Answer:

\(\angle QRT\) and \(\angle QRO\)