To determine which pairs of angles in the diagram are vertical angles, let's analyze the image and the relationships between the angles.

Definition of Vertical Angles:

Vertical angles are the pairs of opposite angles formed by the intersection of two lines. They are congruent to each other.

Analysis of the Diagram:

1. Intersection Points:

   • The lines intersect at point $B$.
   • The four lines form angles around $B$, specifically between $AB$, $BC$, $BD$, and $BE$.

2. Angle Relationships:

   • Vertical angles are formed by opposite rays:
     • $\angle ABE$ and $\angle CBD$: These are vertical angles.
     • $\angle ABC$ and $\angle EBD$: These are also vertical angles.

3. Answer: The correct pairs of vertical angles are:

   • $\angle ABE$ and $\angle CBD$
   • $\angle ABC$ and $\angle EBD$

Would you like me to explain further why these specific pairs are vertical angles or explore related geometric concepts?

Related Questions:

1. What are adjacent angles, and how are they different from vertical angles?
2. How can we use the properties of vertical angles to solve for unknown values in the diagram?
3. What does it mean for vertical angles to be congruent, and how can this property help in proofs?
4. Can you identify supplementary angle pairs in the diagram?
5. How do intersecting lines create a total of 360 degrees around a point?

Tip: Vertical angles are always equal, so they are great for finding unknown angle measures in geometry problems.