Question

and hj are parallel lines. which angles are adjacent angles? ∠gfd and ∠efi ∠gfd and ∠hik ∠gfd and ∠hif ∠gfd and ∠efd

Explanation:

Step1: Recall adjacent - angle definition

Adjacent angles share a common vertex and a common side, and have no interior points in common.

Step2: Analyze each option

• $\angle GFD$ and $\angle EFI$: They share the common vertex $F$, but they are vertical - angles (opposite angles formed by the intersection of two lines), not adjacent angles.
• $\angle GFD$ and $\angle HIK$: They are not related in terms of sharing a common vertex and side, they are just two angles in the figure with no adjacent - angle relationship.
• $\angle GFD$ and $\angle HIF$: They do not share a common vertex and side in the way required for adjacent angles.
• $\angle GFD$ and $\angle EFD$: They share the common vertex $F$ and the common side $FD$, and have no interior points in common. So they are adjacent angles.

Answer:

$\angle GFD$ and $\angle EFD$