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