Two angles are adjacent if they have a common side, a common vertex, and do not overlap. Two angles are vertical if they are non-adjacent and formed by the intersection of two straight lines or segments.
∠ x and ∠ z
Practice makes perfect
We want to determine whether the given angles are adjacent, vertical, or neither. Let's start by recalling the definitions of adjacent angles and vertical angles.
Adjacent Angles
Vertical Angles
Two angles are adjacent if they have a common side, a common vertex, and do not overlap.
Two angles are vertical if they are non-adjacent and formed by the intersection of two straight lines or segments.
Let's now consider the given diagram.
We want to list each angle adjacent to ∠ w. From the diagram, we can see that ∠ x and ∠ z have a common side and a common vertex with ∠ w. They also do not overlap. Therefore, these angles are adjacent angles to ∠ w.
