Final answer:
Angle ABC and angle CBD form a linear pair, and angle CBD and angle DBE form another linear pair. However, angle ABC and DBE are not vertical angles because they do not meet the definition of being non-adjacent angles formed by the intersection of two lines.
Step-by-step explanation:
When we speak of linear pairs in geometry, we're referring to two adjacent angles that are formed when two lines intersect and form a straight line, summing to 180°. Similarly, vertical angles are the opposite angles made by two intersecting lines, and they are always equal to each other. However, vertical angles do not have to be adjacent and do not form linear pairs.
Given that angle ABC and angle CBD form a linear pair, and angle CBD and angle DBE also form a linear pair, we can understand that these angles are indeed adjacent to one another and their measures add up to 180° each. But regarding whether angle ABC and angle DBE are vertical angles, the answer is no. They are not vertical angles because they are not the non-adjacent pairs of angles formed by the intersection of two lines; instead, they are part of consecutive linear pairs that share a common angle, CBD.