Given intersecting lines that form angles labeled $AFE$, $BFC$, $CFD$, $DFE$, and $EFA$, which pair of angles are vertical angles?

• A. $AFE$ and $BFD$
• B. $BFC$ and $EFA$
• C. $AFE$ and $CFD$
• D. $BFC$ and $DFE$

Answer: (C)

Verified step by step guidance

1. Recall that vertical angles are pairs of opposite angles formed when two lines intersect. They share a common vertex and their sides form two pairs of opposite rays.
2. Identify the vertex point where the lines intersect, which is point F in this problem.
3. Look at the given angles around point F: \( \angle AFE \), \( \angle BFC \), \( \angle CFD \), \( \angle DFE \), and \( \angle EFA \).
4. Determine which pairs of these angles are opposite each other, meaning their sides extend in exactly opposite directions from point F.
5. Conclude that the pair of angles that are vertical angles are those whose sides form opposite rays, specifically \( \angle AFE \) and \( \angle CFD \).