Chapter 12.5, Problem 43E

Exercises 41–44 refer to Illustration 16. $\stackrel{\leftrightarrow }{AB}$

and $\stackrel{\leftrightarrow }{AC}$

are secants; $\overline{CD}$

and $\overline{BF}$

are chords.

ILLUSTRATION 16

Suppose $\angle BEC=78°$ and $\stackrel{⌢}{BC}=142°$. Find the measure of $\stackrel{⌢}{DF}$.