Question

select all the pairs of corresponding angles.
∠efd and ∠hif
∠hik and ∠efi
∠jik and ∠gfi
∠gfd and ∠jif

Explanation:

Step1: Recall corresponding - angles definition

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

Step2: Analyze each pair

• For ∠EFD and ∠HIF: They are in the same relative position with respect to the transversal DK and the parallel lines EG and HJ, so they are corresponding angles.
• For ∠HIK and ∠EFI: They are in the same relative position with respect to the transversal DK and the parallel lines EG and HJ, so they are corresponding angles.
• For ∠JIK and ∠GFI: They are in the same relative position with respect to the transversal DK and the parallel lines EG and HJ, so they are corresponding angles.
• For ∠GFD and ∠JIF: They are in the same relative position with respect to the transversal DK and the parallel lines EG and HJ, so they are corresponding angles.

Answer:

∠EFD and ∠HIF, ∠HIK and ∠EFI, ∠JIK and ∠GFI, ∠GFD and ∠JIF