Question

ln and oq are parallel lines. which angles are supplementary angles? ∠lmp and ∠lmk ∠lmp and ∠nmk ∠lmp and ∠opr ∠lmp and ∠qpm

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze \(\angle LMP\) and \(\angle LMK\)

\(\angle LMP\) and \(\angle LMK\) form a linear pair. A linear pair of angles is supplementary. So \(\angle LMP+\angle LMK = 180^{\circ}\)

Step3: Analyze \(\angle LMP\) and \(\angle NMK\)

\(\angle NMK\) and \(\angle LMK\) are vertical angles (\(\angle NMK=\angle LMK\) by the vertical - angles theorem). But \(\angle LMP+\angle NMK=\angle LMP+\angle LMK = 180^{\circ}\) (since \(\angle LMP\) and \(\angle LMK\) are a linear pair)

Step4: Analyze \(\angle LMP\) and \(\angle OPR\)

\(\angle OPR\) and \(\angle MPQ\) are vertical angles (\(\angle OPR = \angle MPQ\)). There is no direct relation to make \(\angle LMP+\angle OPR=180^{\circ}\)

Step5: Analyze \(\angle LMP\) and \(\angle QPM\)

\(\angle LMP\) and \(\angle QPM\) are not in a linear - pair or have any relation that would make their sum \(180^{\circ}\)

Answer:

\(\angle LMP\) and \(\angle LMK\), \(\angle LMP\) and \(\angle NMK\)