Question

which angle is adjacent to $\angle cfd$?
$\angle efa$ $\angle cfa$ $\angle dfe$ $\angle cfe$

Explanation:

Step1: Recall adjacent angles definition

Adjacent angles share a common side and vertex, and their non - common sides form a linear pair (or are adjacent rays). For \(\angle CFD\), the vertex is \(F\), and the sides are \(FC\) and \(FD\).

Step2: Analyze each option

• For \(\angle EFA\): The sides are \(FE\) and \(FA\), no common side with \(\angle CFD\), so not adjacent.
• For \(\angle CFA\): The sides are \(FC\) and \(FA\), no common side (other than \(F\)) with \(\angle CFD\)'s sides \(FC\) and \(FD\) in a way that forms adjacent angles, so not adjacent.
• For \(\angle DFE\): The sides are \(FD\) and \(FE\), no common side with \(\angle CFD\)'s \(FC\) (the other side of \(\angle CFD\)), so not adjacent.
• For \(\angle CFE\): The angle \(\angle CFD\) has sides \(FC\) and \(FD\), and \(\angle CFE\) has sides \(FC\) and \(FE\), but wait, no - wait, \(\angle CFD\) and \(\angle CFE\) share the common side \(FC\) and the vertex \(F\), and the non - common sides \(FD\) and \(FE\) are adjacent to \(FC\). Wait, no, let's re - check. Wait, \(\angle CFD\) and \(\angle DFE\)? No, wait, the correct adjacent angle: \(\angle CFD\) and \(\angle CFE\)? Wait, no, let's look at the rays. The angle \(\angle CFD\) is between \(FC\) and \(FD\). The angle \(\angle CFE\) is between \(FC\) and \(FE\)? No, wait, the options: Wait, \(\angle CFE\) has sides \(FC\) and \(FE\), but \(\angle CFD\) has sides \(FC\) and \(FD\). Wait, maybe I made a mistake. Wait, adjacent angles share a common side and a common vertex, and their non - common sides are adjacent (form a linear pair or are next to each other). So for \(\angle CFD\) (vertex \(F\), sides \(FC\) and \(FD\)), the angle that shares the common side \(FC\) or \(FD\) and the vertex \(F\). Let's check \(\angle CFE\): No, \(\angle DFE\): No. Wait, \(\angle CFE\) - wait, the correct answer is \(\angle CFE\)? Wait, no, let's re - examine. Wait, the angle \(\angle CFD\) and \(\angle CFE\): Wait, no, the angle \(\angle CFD\) and \(\angle DFE\) share \(FD\), but \(\angle DFE\) is between \(FD\) and \(FE\). Wait, no, the correct adjacent angle to \(\angle CFD\) is \(\angle CFE\)? Wait, no, let's look at the options again. Wait, the angle \(\angle CFD\) and \(\angle CFE\) share the side \(FC\), and the vertex \(F\), and the other sides \(FD\) (of \(\angle CFD\)) and \(FE\) (of \(\angle CFE\)) are adjacent to \(FC\). Wait, but actually, the correct adjacent angle is \(\angle CFE\)? Wait, no, let's think again. Adjacent angles are two angles that share a common side and a common vertex, and their interiors do not overlap. So for \(\angle CFD\) (sides \(FC\) and \(FD\)), the angle that shares \(FC\) and \(F\) and has the other side adjacent to \(FD\). Wait, \(\angle CFE\) has side \(FC\) and \(FE\), but \(FD\) and \(FE\) are on the same side? No, maybe I messed up. Wait, the correct answer is \(\angle CFE\)? Wait, no, let's check the options. Wait, the angle \(\angle CFD\) and \(\angle CFE\): Wait, no, the angle \(\angle CFD\) and \(\angle DFE\) share \(FD\), but \(\angle DFE\) is between \(FD\) and \(FE\). Wait, no, the correct answer is \(\angle CFE\). Wait, maybe I was wrong earlier. Let's recall: Adjacent angles share a common side and a common vertex. So \(\angle CFD\) (vertex \(F\), sides \(FC\) and \(FD\)) and \(\angle CFE\) (vertex \(F\), sides \(FC\) and \(FE\)) share the common side \(FC\) and the common vertex \(F\), and their non - common sides \(FD\) and \(FE\) are adjacent to \(FC\). So \(\angle CFE\) is adjacent to \(\angle CFD\).

Answer:

\(\angle CFE\)