Question

which angles are alternate interior angles?
options:
$\angle pqs$ and $\angle mnq$
$\angle pqn$ and $\angle pqs$
$\angle rqn$ and $\angle pqs$
$\angle pqn$ and $\angle onq$

Explanation:

Step1: Recall Alternate Interior Angles Definition

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two parallel lines, on opposite sides of the transversal, and are congruent.

Step2: Analyze Each Option

• Option 1: $\angle PQS$ and $\angle MNQ$: $\angle PQS$ is at $Q$, $\angle MNQ$ is at $N$. These are not between the two parallel lines (OM and PR) in the correct positions.
• Option 2: $\angle PQN$ and $\angle PQS$: These are adjacent angles at $Q$, forming a linear pair, not alternate interior angles.
• Option 3: $\angle RQN$ and $\angle PQS$: $\angle RQN$ is on one side, $\angle PQS$ on the other, but not between the lines correctly.
• Option 4: $\angle PQN$ and $\angle ONQ$: Lines OM and PR are parallel, transversal is LS. $\angle PQN$ is between PR and OM, on one side of LS; $\angle ONQ$ is between OM and PR, on the other side of LS. So they are alternate interior angles.

Answer:

$\angle PQN$ and $\angle ONQ$