It is given that the measure of arc BC is 182 degrees
that is
[tex]b=182^0[/tex]
the measure of arc AC is 78 degrees.
That is
[tex]a=78^0[/tex]
We know that
[tex]\angle1=\frac{1}{2}(b-a)[/tex]
Hence
[tex]\begin{gathered} \angle1=\frac{1}{2}(182^0-78^0) \\ \\ \angle1=\frac{1}{2}(104) \\ \angle1=52^0 \end{gathered}[/tex]
Hence 52 degrees is the correct answer.
