Question: Which angles are vertical angles?
The diagram shows two intersecting lines at point $I$ and another pair of intersecting lines at point $F$, with labeled points $H$, $I$, $J$ on the left slanted line, $E$, $F$, $G$ on the right slanted line, and $K$, $I$, $F$, $D$ on the diagonal line.
$\angle GFI$ and $\angle JIK$
$\angle HIK$ and $\angle GFI$
$\angle EFI$ and $\angle HIK$
$\angle HIF$ and $\angle JIK$
1. **Problem Statement:** Identify which pairs of angles are vertical angles from the given options.
2. **Definition:** Vertical angles are the pairs of opposite angles made by two intersecting lines. They are always equal.
3. **Step-by-step Analysis:**
- At point $I$, two lines intersect, creating angles such as $\angle HIK$, $\angle JIK$, $\angle HIF$, and $\angle GFI$.
- At point $F$, two lines intersect, creating angles such as $\angle GFI$, $\angle EFI$, and $\angle HIF$.
4. **Check each pair:**
- $\angle GFI$ and $\angle JIK$: These angles are at different intersection points ($F$ and $I$), so they are not vertical angles.
- $\angle HIK$ and $\angle GFI$: These angles are at different points ($I$ and $F$), so not vertical angles.
- $\angle EFI$ and $\angle HIK$: Different points ($F$ and $I$), so not vertical angles.
- $\angle HIF$ and $\angle JIK$: Both angles share vertex $I$ and are opposite each other formed by intersecting lines at $I$, so these are vertical angles.
5. **Conclusion:** The pair of vertical angles is $\boxed{\angle HIF \text{ and } \angle JIK}$.