Question

which angles are supplementary angles?
∠qrt and ∠sro , ∠nor and ∠nom
∠nom and ∠por ∠qro and ∠srt

Explanation:

Step1: Recall Supplementary Angles

Supplementary angles sum to \(180^\circ\) (a straight line). We analyze each pair:

Step2: Analyze \(\angle QRT\) and \(\angle SRO\)

These are vertical angles (opposite each other at intersection), so they are equal, not supplementary (unless each is \(90^\circ\), but no info suggests that).

Step3: Analyze \(\angle NOR\) and \(\angle NOM\)

\(\angle NOR\) and \(\angle NOM\) form a linear pair (they are adjacent and on a straight line \(TM\)), so their sum is \(180^\circ\). Thus, they are supplementary.

Step4: Analyze \(\angle NOM\) and \(\angle POR\)

\(\angle NOM\) and \(\angle POR\) are alternate angles (since \(QS \parallel NP\) and \(TM\) is transversal), so they are equal, not supplementary.

Step5: Analyze \(\angle QRO\) and \(\angle SRT\)

These are vertical angles, so they are equal, not supplementary.

Answer:

\(\angle NOR\) and \(\angle NOM\)