Question

ln and oq are parallel lines. which angles are alternate exterior angles? ∠lmk and ∠nmp ∠opr and ∠opm ∠qpr and ∠lmk ∠qpm and ∠lmp

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 option

• For \(\angle LMK\) and \(\angle NMP\): These angles are adjacent, so they are not alternate exterior angles.
• For \(\angle OPR\) and \(\angle OPM\): These angles are adjacent, so they are not alternate exterior angles.
• For \(\angle QPR\) and \(\angle LMK\): These angles do not lie in the correct position (not outside the two parallel lines in the required way) to be alternate exterior angles.
• For \(\angle QPM\) and \(\angle LMP\): \(\overleftrightarrow{LN}\parallel\overleftrightarrow{OQ}\) and \(\overleftrightarrow{KR}\) is the transversal. \(\angle QPM\) and \(\angle LMP\) are non - adjacent, lie outside the parallel lines \(\overleftrightarrow{LN}\) and \(\overleftrightarrow{OQ}\), and on opposite sides of the transversal \(\overleftrightarrow{KR}\).

Answer:

\(\angle QPM\) and \(\angle LMP\)