Question

Are arcs BE and CD congruent? YES NO Explain your thinking

Answer 1

Since we're looking at half a circumference, we can conclude that

$\angle CAD+80+50=180$

Solving for angle CAD,

$\begin{gathered} \angle CAD+80+50=180 \\ \rightarrow\angle CAD=180-80-50 \\ \rightarrow\angle CAD=50 \end{gathered}$

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.