Answer:
Option B. [tex]146\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m<DEB=\frac{1}{2}(arc \ BCD)[/tex]
substitute the values
[tex]107\°=\frac{1}{2}(arc \ BCD)[/tex]
[tex]arc \ BCD=214\°[/tex]
Remember that
[tex]arc \ DEB+arc \ BCD=360\°[/tex] -----> complete circle
substitute the value of arc BCD and solve for arc DEB
[tex]arc \ DEB+214\°=360\°[/tex]
[tex]arc \ DEB=360\°-214\°=146\°[/tex]
