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.
Example Solution: ∠ 1 and ∠ 2, ∠ 5 and ∠ 4
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 can see that ∠ 1 and ∠ 2 have a common side, a common vertex, and they do not overlap. The same is true for ∠ 5 and ∠ 4. Therefore, these pairs of angles are adjacent angles. Be aware that this is only one possible answer because there are more adjacent angles in the given diagram.
