Question

which angles are alternate interior angles?
∠ihk and ∠lkm ∠ihk and ∠lkh
∠lkh and ∠ghk ∠ghf and ∠ghk

Explanation:

Step1: Recall Alternate Interior Angles

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

Step2: Analyze Each Option

• Option 1: $\angle IHK$ and $\angle LKM$: $\angle LKM$ is an exterior - like angle (not between the two parallel lines $JL$ and $GI$), so not alternate interior.
• Option 2: $\angle IHK$ and $\angle LKH$: The transversal is $MF$ (the line with points $M, K, H, F$), and the two parallel lines are $JL$ (with points $J, K, L$) and $GI$ (with points $G, H, I$). $\angle IHK$ and $\angle LKH$ lie between the two parallel lines and on opposite sides of the transversal $MF$.
• Option 3: $\angle LKH$ and $\angle GHK$: These two angles are on the same side of the transversal, so not alternate interior.
• Option 4: $\angle GHF$ and $\angle GHK$: These are adjacent angles, not alternate interior.

Answer:

$\angle IHK$ and $\angle LKH$