step 1 find the measure of arc AC we know that <span>The inscribed angle measures half of the arc it comprises. </span>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 <span>The measure of the interior angle is the half-summit of the arcs that comprise it and its opposite. </span>so m∠DEC=(1/2)*[arc AB+arc DC]