arc AC = 72°
arc BD = 108°
∠DEB = 90°
Explanation:
AC:CB:BD:DA = 4:2:6:8
ratio of AC = 4
ratio of CB = 2
ratio of BD = 6
ratio of DA = 8
Total ratio = 4 + 2 + 6 + 8 = 20
Total angles in a circle = 360°
[tex]\begin{gathered} arcAC=\frac{ratio\text{ of AC}}{total\text{ ratio}}\times360\degree \\ \text{arc AC = }\frac{4}{20}\times360\text{ =}\frac{1440}{20} \\ \text{arc AC = }72\degree \end{gathered}[/tex][tex]\begin{gathered} \text{arc BD = }\frac{ratio\text{ of BD}}{\text{total ratio}}\times360\degree \\ \text{arc BD = }\frac{6}{20}\times360\degree\text{ =}\frac{2160}{20} \\ \text{arc BD = 108}\degree \end{gathered}[/tex]
Intersecting chord theorem:
∠DEB = 1/2(arc BD + arc AC)
∠DEB = 1/2(108 + 72)
∠DEB = 1/2(180)
∠DEB = 90°
