To determine which choice includes two pairs of adjacent angles from the coordinate plane, consider the geometric definition of adjacent angles. Adjacent angles share a common side and a common vertex, but they do not overlap.
Let's analyze each choice:
1. [tex]$\angle 1$[/tex] and [tex]$\angle 4, \angle 2$[/tex] and [tex]$\angle 5$[/tex]
To verify if these are pairs of adjacent angles:
- [tex]$\angle 1$[/tex] and [tex]$\angle 4$[/tex]: These angles must share a common side and vertex.
- [tex]$\angle 2$[/tex] and [tex]$\angle 5$[/tex]: These angles must share a common side and vertex.
2. [tex]$\angle 6$[/tex] and [tex]$\angle 5, \angle 3$[/tex] and [tex]$\angle 2$[/tex]
To verify if these are pairs of adjacent angles:
- [tex]$\angle 6$[/tex] and [tex]$\angle 5$[/tex]: These angles must share a common side and vertex.
- [tex]$\angle 3$[/tex] and [tex]$\angle 2$[/tex]: These angles must share a common side and vertex.
3. [tex]$\angle 6$[/tex] and [tex]$\angle 4, \angle 11$[/tex] and [tex]$\angle 4$[/tex]
To verify if these are pairs of adjacent angles:
- [tex]$\angle 6$[/tex] and [tex]$\angle 4$[/tex]: These angles must share a common side and vertex.
- [tex]$\angle 11$[/tex] and [tex]$\angle 4$[/tex]: These angles must share a common side and vertex.
4. [tex]$\angle 4$[/tex] and [tex]$\angle 5, \angle 2$[/tex] and [tex]$\angle 16$[/tex]
To verify if these are pairs of adjacent angles:
- [tex]$\angle 4$[/tex] and [tex]$\angle 5$[/tex]: These angles must share a common side and vertex.
- [tex]$\angle 2$[/tex] and [tex]$\angle 16$[/tex]: These angles must share a common side and vertex.
The choice [tex]$\angle 1$[/tex] and [tex]$\angle 4, \angle 2$[/tex] and [tex]$\angle 5$[/tex] includes two pairs of adjacent angles.
