Question

which are vertical angles?
○ ∠afe and ∠bfd
○ ∠bfc and ∠dfe
○ ∠afe and ∠cfd
○ ∠bfc and ∠efa

Explanation:

Vertical angles are formed by two intersecting lines and are opposite each other, sharing a common vertex but no common side. Let's analyze each option:

• Option 1: $\angle AFE$ and $\angle BFD$: These angles are formed by the intersection of lines $AE$ and $BD$ (or relevant intersecting lines) and are opposite each other, sharing vertex $F$ with no common side.
• Option 2: $\angle BFC$ and $\angle DFE$: These do not fit the vertical angles definition as they are not opposite each other from intersecting lines.
• Option 3: $\angle AFE$ and $\angle CFD$: These are not opposite each other from intersecting lines.
• Option 4: $\angle BFC$ and $\angle EFA$: These are not opposite each other from intersecting lines.

So, $\angle AFE$ and $\angle BFD$ are vertical angles.

Answer:

A. $\angle AFE$ and $\angle BFD$