the complete question in the attached figure
we know that
step 1
find the measure of arc AC
we know that
The inscribed angle measures half of the arc it comprises.
so
m∠GAC=(1/2)*[arc AC]
m∠GAC=75°
(1/2)*arc AC=75°-----> arc AC=150°
step 2
find the arc DC
arc AC=arc AD+arc DC
arc DC=arc AC-arc AD----> arc DC=150°-52°----> arc DC=98°
step 3
find m∠DEC
we know that
The measure of the interior angle is the half-summit of the arcs that comprise it and its opposite.
so
m∠DEC=(1/2)*[arc AB+arc DC]
arc AB=88°
arc DC=98°
m∠DEC=(1/2)*[88+98]----->
m∠DEC=93°
the answer is
m∠DEC=93°