Answer:
m(arc AC) = 72°
m(arc BD) = 108°
m∠DEB = 90°
Step-by-step explanation:
Ratio of the measure of arc AC, arc BC, arc BD and arc AD = 4 : 2 : 6 : 8
Since, m(arc AC) + m(arc CB) + m(arc BD) + m(arc AD) = 360°
By the property of ratio,
Measure of arc AC = [tex]\frac{4}{4+2+6+8}\times (360^0)[/tex]
= [tex]\frac{4\times 360}{20}[/tex]
= 72°
Measure of arc BD = [tex]\frac{6}{4+2+6+8}\times (360^0)[/tex]
= [tex]\frac{6\times 360}{20}[/tex]
= 108°
Measure of ∠DEB = [tex]\frac{1}{2}m(arcAC + arc BD)[/tex]
= [tex]\frac{1}{2}(72+108)[/tex]
= 90°