Part A: Solving for angle measure A
Part B: Finding Arc CE
[tex]\begin{gathered} m\angle B=\frac{1}{2}\text{Arc }CE \\ 24\degree=\frac{1}{2}\text{Arc }CE \\ \text{Arc }CE=2\cdot24\degree \\ \\ \text{Therefore, Arc }CE=48° \end{gathered}[/tex]
Part C: Finding ang measure C
[tex]\begin{gathered} m\angle C=\frac{1}{2}\text{Arc }BD \\ m\angle C=\frac{1}{2}(82\degree) \\ \\ \text{Therefore, }m\angle C=41° \end{gathered}[/tex]
Part D: angle measure D
[tex]\begin{gathered} m\angle D=\frac{1}{2}\text{Arc }AC \\ m\angle D=\frac{1}{2}(74\degree) \\ m\angle D=\frac{1}{2}(74\degree) \\ \\ \text{Therefore, }m\angle D=37° \end{gathered}[/tex]
Part E: angle measure ABE
[tex]\begin{gathered} m\angle ABE=\frac{1}{2}\text{Arc AE} \\ m\angle ABE=\frac{1}{2}(\text{Arc AC}+\text{Arc CE}) \\ m\angle ABE=\frac{1}{2}(74\degree+48\degree) \\ m\angle ABE=\frac{1}{2}(122°) \\ \\ \text{Therefore, }m\angle ABE=61° \end{gathered}[/tex]
