Question

fh and ik are parallel lines. which angles are alternate exterior angles? ∠hge and ∠ijl ∠hge and ∠kjg ∠fge and ∠fgj ∠fge and ∠ijg

Explanation:

Step1: Recall the definition of alternate exterior angles

Alternate exterior angles are non - adjacent angles that lie outside the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each option

• For $\angle HGE$ and $\angle IJL$:
• $\overrightarrow{FH}\parallel\overrightarrow{IK}$, and $EL$ is the transversal.
• $\angle HGE$ and $\angle IJL$ lie outside $\overrightarrow{FH}$ and $\overrightarrow{IK}$ and on opposite sides of the transversal $EL$.
• For $\angle HGE$ and $\angle KJG$: $\angle KJG$ is not an exterior angle with respect to the parallel lines $\overrightarrow{FH}$ and $\overrightarrow{IK}$.
• For $\angle FGE$ and $\angle FGJ$: These angles are adjacent, not alternate exterior angles.
• For $\angle FGE$ and $\angle IJG$: $\angle FGE$ is an exterior angle, but $\angle IJG$ is an interior angle.

Answer:

$\angle HGE$ and $\angle IJL$