1. **Problem Statement:** Given two parallel lines NP and QS, and a transversal line TROM crossing them at points R and O, identify which pairs of angles are supplementary. 2. **Key Concept:** Supplementary angles are two angles whose measures add up to 180 degrees. 3. **Step 1: Understand the setup.** - Lines NP and QS are parallel. - Line TROM is a transversal crossing these parallel lines at points R and O. 4. **Step 2: Identify angle pairs formed by the transversal and parallel lines.** - At point R on line QS, angles include \(\angle QRO\), \(\angle SRT\), and \(\angle SRO\). - At point O on line NP, angles include \(\angle POR\), \(\angle NOM\). 5. **Step 3: Use properties of parallel lines and transversals.** - Consecutive interior angles are supplementary. - Linear pairs (adjacent angles on a straight line) are supplementary. 6. **Step 4: Analyze each pair:** - \(\angle QRO\) and \(\angle SRT\): These are adjacent angles on the same side of the transversal at point R, forming a linear pair. Therefore, they are supplementary. - \(\angle QRO\) and \(\angle SRO\): These two angles share vertex R and side RO but are adjacent angles on the same line segment QS, so they are not supplementary but complementary or adjacent angles. - \(\angle QRO\) and \(\angle POR\): These angles are on opposite sides of the transversal but at different points (R and O). They are not supplementary. - \(\angle QRO\) and \(\angle NOM\): These angles are on different parallel lines and not adjacent or consecutive interior angles, so they are not supplementary. 7. **Final answer:** The supplementary angles are \(\angle QRO\) and \(\angle SRT\).