In the given problem the line DE passes through the center of the circle hence the line DE is the diameter of the circle.
From the property of the circle the angle subtended by the diameter on the circle is a right angle.
Hence angle DFE is 90 degrees.
In triangle DFE,
![\begin{gathered} \angle DFE+\angle EDF+\angle DEF=180^(\circ) \\ 90^(\circ)+\angle EDF+63^(\circ)=180^(\circ) \\ \angle EDF=180^(\circ)-153^(\circ) \\ \angle EDF=27^(\circ) \end{gathered}]()
Thus, the arc FE subtends 27 degrees at the circle.