Since we're looking at half a circumference, we can conclude that
[tex]\angle CAD+80+50=180[/tex]
Solving for angle CAD,
[tex]\begin{gathered} \angle CAD+80+50=180 \\ \rightarrow\angle CAD=180-80-50 \\ \rightarrow\angle CAD=50 \end{gathered}[/tex]
Now, since arcs BE and CD sustain the same angle and are on the same circumference (same radius), we can conclude that they are indeed congruent.
