Question

which angles are alternate interior angles? image of lines and angles ∠kjm and ∠ijm; ∠kjm and ∠nmo; ∠nmj and ∠ijm; ∠ijh and ∠nmj

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 (interior) and on opposite sides of the transversal (alternate).

Step2: Analyze Each Option

• Option 1: $\angle KJM$ and $\angle IJM$: These angles are adjacent (share a common side and vertex), not alternate interior.
• Option 2: $\angle KJM$ and $\angle NMO$: $\angle NMO$ is not between the two parallel lines (assuming $LN \parallel IK$), so not interior.
• Option 3: $\angle NMJ$ and $\angle IJM$: $\angle NMJ$ and $\angle IJM$ lie between the parallel lines ($LN$ and $IK$) and on opposite sides of transversal $OH$. This fits the alternate interior angles definition.
• Option 4: $\angle IJH$ and $\angle NMJ$: $\angle IJH$ is above the transversal, not interior (between the parallel lines).

Answer:

$\angle NMJ$ and $\angle IJM$