Question

which angles are vertical angles?
image of intersecting lines with points d, e, f, g, h, i, j, k and angles ∠efd, ∠hik, ∠gfi, ∠jik, ∠hik, ∠jif, ∠jif, ∠gfd as options

Explanation:

Step1: Recall vertical angles definition

Vertical angles are opposite angles formed by two intersecting lines, and they are equal.

Step2: Analyze each option

• Option 1: $\angle EFD$ and $\angle HIK$: These are not opposite angles from intersecting lines.
• Option 2: $\angle GFI$ and $\angle JIK$: These are not opposite angles from intersecting lines.
• Option 3: $\angle HIK$ and $\angle JIF$: When lines $HJ$ and $DK$ intersect at $I$, $\angle HIK$ and $\angle JIF$ are opposite angles (vertical angles).
• Option 4: $\angle JIF$ and $\angle GFD$: These are not opposite angles from intersecting lines.

Answer:

$\angle HIK$ and $\angle JIF$