Question

ln and oq are parallel lines. select all the pairs of alternate exterior angles. ∠lmk and ∠nmp ∠qpr and ∠nmp ∠lmk and ∠qpr ∠opr and ∠nmk

Explanation:

Step1: Recall the definition of alternate exterior angles

Alternate exterior angles are non - adjacent angles that lie outside the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each pair

• For \(\angle LMK\) and \(\angle NMP\): These are vertical angles, not alternate exterior angles.
• For \(\angle QPR\) and \(\angle NMP\): These do not lie outside the parallel lines in the correct alternate exterior position.
• For \(\angle LMK\) and \(\angle QPR\): These do not meet the criteria of alternate exterior angles.
• For \(\angle OPR\) and \(\angle NMK\):
• \(\overleftrightarrow{LN}\parallel\overleftrightarrow{OQ}\) and \(\overleftrightarrow{RK}\) is the transversal.
• \(\angle OPR\) and \(\angle NMK\) lie outside the parallel lines \(\overleftrightarrow{LN}\) and \(\overleftrightarrow{OQ}\) and on opposite sides of the transversal \(\overleftrightarrow{RK}\).

Answer:

\(\angle OPR\) and \(\angle NMK\)