we know that
The inscribed angle measures half that of the arc comprising
in this problem
m∠DGF -----> is a inscribed angle
m∠DGF=[tex]\frac{1}{2}(arc\ DF)[/tex]
we have
[tex]arc\ DF=153\°[/tex]
substitute
m∠DGF=[tex]\frac{1}{2}(153\°)=76.5\°[/tex]
we know that
[tex]arc\ DGF+arc\ DF=360\°[/tex]
Find the measure of arc DGF
[tex]arc\ DGF=360\°-arc\ DF[/tex]
[tex]arc\ DGF=360\°-153\°=207\°[/tex]
therefore
the answer is
a) the measure of inscribed angle m∠DGF is [tex]76.5\°[/tex]
b) the measure of arc DGF is [tex]207\°[/tex]
