Answer: The correct options are
(A) DEF.
(C) FED.
Step-by-step explanation: We are given to select the correct options that describes an angle with a vertex at E.
We know that
while writing the name of an angle, we always write the vertex in the middle and the points on the two legs of the angle are written on the two sides, left and right.
<u><em>Option (A):</em></u> DEF.
Since the vertex E is written in the middle and the points D and F on the two legs ED and EF are written on the left and right side respectively,
so DEF describes an angle with vertex E.
<u><em>Option (B):</em></u> DFE.
Since the vertex E is not written in the middle, so DFE does not describes an angle with vertex E.
<u><em>Option (C):</em></u> FED.
Since the vertex E is written in the middle and the points F and D on the two legs EF and ED are written on the left and right side respectively,
so FED describes an angle with vertex E.
<u><em>Option (D):</em></u> EFD.
Since the vertex E is not written in the middle, so EFD does not describes an angle with vertex E.
Thus, the correct descriptions of an angle with vertex E are DEF and FED. The angle is shown in the attached figure below.
Options (A) and (C) are CORRECT.