Question

which angles are consecutive interior angles?
∠ijg and ∠fgj ∠ijl and ∠ijg
∠kjg and ∠ijg ∠kjl and ∠ijg

Explanation:

Step1: Recall the definition of consecutive interior angles

Consecutive interior angles are two interior angles on the same side of the transversal.

Step2: Analyze each option

• For $\angle IJG$ and $\angle FGJ$: They are on the same side of the transversal $LJ$ and between the two lines $IK$ and $FH$.
• For $\angle IJL$ and $\angle IJG$: $\angle IJL$ is an exterior - related angle (not an interior angle in the sense of consecutive interior angles for the two lines $IK$ and $FH$).
• For $\angle KJG$ and $\angle IJG$: They are adjacent angles forming a linear pair (sum to $180^{\circ}$ as they are on a straight line along the transversal, not consecutive interior angles for the two parallel - like lines).
• For $\angle KJL$ and $\angle IJG$: $\angle KJL$ is an exterior - related angle (not an interior angle in the relevant sense for the two lines $IK$ and $FH$).

Answer:

$\angle IJG$ and $\angle FGJ$