Vertical angles are pairs of opposite angles made by two intersecting lines. In this image, the angles are formed by lines intersecting at point F.

To identify the vertical angles:

• Angles that are directly across from each other at the point of intersection are vertical angles.

Let's go through the options:

1. ∠AFE and ∠BFD: These two angles are opposite each other, so they are vertical angles.

2. ∠BFC and ∠DFE: These angles are not opposite each other; they share the side FC, so they are not vertical angles.

3. ∠AFE and ∠CFD: These angles are not directly opposite each other, so they are not vertical angles.

4. ∠BFC and ∠EFA: These angles are not opposite each other either, so they are not vertical angles.

The correct answer is ∠AFE and ∠BFD (Option 1).

Would you like further details or have any questions?

Here are 5 related questions to deepen understanding:

1. What defines vertical angles and why are they congruent?
2. Can vertical angles ever be supplementary? Why or why not?
3. How do vertical angles relate to parallel lines and transversals?
4. Are all angles formed at an intersection always vertical or complementary? Explain.
5. How can knowing vertical angles help in solving for unknown angle measures?

Tip: Vertical angles are always equal in measure, which makes them useful in various geometric proofs and problems!