From th arc-angle relationships, we know that a vertex angle inside a circle is half the sum of the measures of its intercepted arcs, that is,
[tex]m\angle1=\frac{50+56}{2}[/tex]
which gives
[tex]\begin{gathered} m\angle1=\frac{106}{2} \\ m\angle1=53 \end{gathered}[/tex]
Therefore, the answer is 53 degrees.
