Question

eg and hj are parallel lines. which angles are corresponding angles? ∠jik and ∠hik ∠hik and ∠gfd ∠gfd and ∠gfi ∠hik and ∠efi

Explanation:

Step1: Recall the definition of corresponding angles

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

Step2: Analyze each option

• For $\angle JIK$ and $\angle HIK$: These angles are adjacent, not in corresponding positions.
• For $\angle HIK$ and $\angle GFD$: $\overrightarrow{EG}\parallel\overrightarrow{HJ}$ and $KD$ is the transversal. $\angle HIK$ and $\angle GFD$ are in the same relative position (both above the parallel lines and on the same side of the transversal).
• For $\angle GFD$ and $\angle GFI$: These angles are adjacent, not corresponding.
• For $\angle HIK$ and $\angle EFI$: These angles are not in the same relative position with respect to the parallel lines and the transversal.

Answer:

$\angle HIK$ and $\angle GFD$