Question

Find a. angle measure Ab. mC^Ec. angle measure Cd. angle measure De. angle measure ABE

Answer 1

Part A: Solving for angle measure A

Part B: Finding Arc CE

`\begin{gathered} m\angle B=(1)/(2)\text{Arc }CE \\ 24\degree=(1)/(2)\text{Arc }CE \\ \text{Arc }CE=2\cdot24\degree \\ \\ \text{Therefore, Arc }CE=48° \end{gathered}`

Part C: Finding ang measure C

`\begin{gathered} m\angle C=(1)/(2)\text{Arc }BD \\ m\angle C=(1)/(2)(82\degree) \\ \\ \text{Therefore, }m\angle C=41° \end{gathered}`

Part D: angle measure D

`\begin{gathered} m\angle D=(1)/(2)\text{Arc }AC \\ m\angle D=(1)/(2)(74\degree) \\ m\angle D=(1)/(2)(74\degree) \\ \\ \text{Therefore, }m\angle D=37° \end{gathered}`

Part E: angle measure ABE

`\begin{gathered} m\angle ABE=(1)/(2)\text{Arc AE} \\ m\angle ABE=(1)/(2)(\text{Arc AC}+\text{Arc CE}) \\ m\angle ABE=(1)/(2)(74\degree+48\degree) \\ m\angle ABE=(1)/(2)(122°) \\ \\ \text{Therefore, }m\angle ABE=61° \end{gathered}`