Question

fh and ik are parallel lines. which angles are corresponding angles? ∠hgj and ∠kjl ∠hgj and ∠kjg ∠hgj and ∠ijl ∠hgj and ∠hge

Explanation:

Step1: Recall the definition of corresponding angles

Corresponding angles are angles that are in the same relative position with respect to the parallel lines and the transversal.

Step2: Analyze each option

• For $\angle HGJ$ and $\angle KJL$:
• $\angle HGJ$ is at the intersection of line $FH$ and transversal $EL$, and $\angle KJL$ is at the intersection of line $IK$ and transversal $EL$.
• They are in the same relative position (both are on the same side of the transversal and on the "lower - right" side with respect to the parallel lines $FH$ and $IK$).
• For $\angle HGJ$ and $\angle KJG$:
• $\angle HGJ$ and $\angle KJG$ are alternate interior angles (they are between the parallel lines and on opposite sides of the transversal).
• For $\angle HGJ$ and $\angle IJL$:
• $\angle IJL$ is not in the same relative position as $\angle HGJ$ with respect to the parallel lines and the transversal.
• For $\angle HGJ$ and $\angle HGE$:
• $\angle HGJ$ and $\angle HGE$ are adjacent angles (they share a common side).

Answer:

$\angle HGJ$ and $\angle KJL$