Question

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

Explanation:

Step1: Recall the definition of alternate exterior angles

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

Step2: Analyze each pair of angles

• For \(\angle OPR\) and \(\angle HMK\): \(\overleftrightarrow{LN}\parallel\overleftrightarrow{OQ}\) and \(\overleftrightarrow{RK}\) is the transversal. \(\angle OPR\) and \(\angle HMK\) lie outside the parallel lines \(\overleftrightarrow{LN}\) and \(\overleftrightarrow{OQ}\) and on opposite sides of the transversal \(\overleftrightarrow{RK}\).
• For \(\angle OPR\) and \(\angle LMK\): \(\angle LMK\) does not satisfy the "outside" condition for alternate exterior angles with respect to \(\overleftrightarrow{LN}\) and \(\overleftrightarrow{OQ}\) and transversal \(\overleftrightarrow{RK}\).
• For \(\angle OPR\) and \(\angle LMP\): \(\angle LMP\) does not satisfy the "outside" condition for alternate exterior angles with respect to \(\overleftrightarrow{LN}\) and \(\overleftrightarrow{OQ}\) and transversal \(\overleftrightarrow{RK}\).
• For \(\angle OPR\) and \(\angle QPR\): These two angles are adjacent, so they cannot be alternate exterior angles.

Answer:

\(\angle OPR\) and \(\angle HMK\)