Question

select all the pairs of adjacent angles.
∠hif and ∠efi
∠hik and ∠jik
∠hik and ∠efd
∠hik and ∠hif

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 pair

• For $\angle HIF$ and $\angle EFI$: They share vertex $I$, common - side $FI$, and no interior points in common, so they are adjacent.
• For $\angle HIK$ and $\angle JIK$: They share vertex $I$, common - side $IK$, and no interior points in common, so they are adjacent.
• For $\angle HIK$ and $\angle EFD$: They do not share a common vertex or a common side, so they are not adjacent.
• For $\angle HIK$ and $\angle HIF$: They share vertex $I$, common - side $HI$, and no interior points in common, so they are adjacent.

Answer:

$\angle HIF$ and $\angle EFI$, $\angle HIK$ and $\angle JIK$, $\angle HIK$ and $\angle HIF$