Question

which angles are corresponding angles? ∠hif and ∠efi ∠hif and ∠gfd ∠hif and ∠jik ∠hif and ∠efd

Explanation:

Step1: Recall corresponding - angles definition

Corresponding angles are in the same relative position with respect to the transversal and the parallel lines. When a transversal intersects two parallel lines, corresponding angles are congruent.

Step2: Analyze each option

• $\angle HIF$ and $\angle EFI$ are alternate - interior angles.
• $\angle HIF$ and $\angle GFD$ are corresponding angles. $\angle HIF$ and $\angle GFD$ are both on the same side of the transversal $DK$ and on the same relative side of the lines $HJ$ and $EG$ respectively.
• $\angle HIF$ and $\angle JIK$ are vertical angles.
• $\angle HIF$ and $\angle EFD$ are not in a corresponding - angles relationship.

Answer:

$\angle HIF$ and $\angle GFD$