Question

which angles are consecutive interior angles? ∠ihk and ∠jkh ∠ihk and ∠ihf ∠ihk and ∠lkh ∠ihk and ∠ghk

Explanation:

Step1: Recall definition of consecutive - interior angles

Consecutive - interior angles are two angles that lie between two lines and on the same side of a transversal.

Step2: Analyze each option

For $\angle IHK$ and $\angle JKH$: $\angle IHK$ and $\angle JKH$ lie between lines $GI$ and $JL$ and on the same side of transversal $FM$, so they are consecutive - interior angles.
For $\angle IHK$ and $\angle IHF$: $\angle IHF$ is an exterior angle with respect to the lines $GI$ and $JL$ and transversal $FM$, so they are not consecutive - interior angles.
For $\angle IHK$ and $\angle LKH$: $\angle LKH$ is on the opposite side of the transversal $FM$ compared to $\angle IHK$ with respect to the lines $GI$ and $JL$, so they are not consecutive - interior angles.
For $\angle IHK$ and $\angle GHK$: $\angle GHK$ and $\angle IHK$ are adjacent angles, not consecutive - interior angles.

Answer:

$\angle IHK$ and $\angle JKH$