the complete question in the attached figure
we know that
angle < DF is an inscribed angle.
An inscribed angle is an angle with its vertex on the circle which is formed by two intersecting chords.
The inscribed angle measures half of the arc it comprises
the arc it comprises is the arc DF
the arc DF is equal to
[tex](360-52)=308degrees[/tex]
Hence
∡DF is equal to arc DF/2
[tex](308/2)=154degrees[/tex]
the answer is
∡DF=[tex]154[/tex]°
