Question

which angles are alternate interior angles?\
$\angle pqn$ and $\angle mnl$\
$\angle pqn$ and $\angle onq$\
$\angle pqn$ and $\angle onl$\
$\angle pqn$ and $\angle rqn$

Explanation:

To determine alternate interior angles, we recall the definition: alternate interior angles are formed when a transversal crosses two parallel lines, lying between the two lines and on opposite sides of the transversal. Here, lines \( PR \) and \( MO \) are parallel (vertical lines with same direction), and \( SL \) is the transversal.

• For \( \angle PQN \) and \( \angle ONQ \): \( \angle PQN \) is between \( PR \) and \( SL \) (left of transversal), \( \angle ONQ \) is between \( MO \) and \( SL \) (right of transversal), and they lie between the two parallel lines. This fits alternate interior angles.
• Other options: \( \angle PQN \) and \( \angle MNL \) are not between the lines; \( \angle PQN \) and \( \angle ONL \) are not both interior; \( \angle PQN \) and \( \angle RQN \) are supplementary (linear pair), not alternate interior.

Answer:

\( \angle PQN \) and \( \angle ONQ \)