Answer:
The part A can be calculate using the secant theorem below
To figure out the value of triangle ADB, we will use the formula below
[tex]\begin{gathered} \angle ADB=\frac{1}{2}(ARC\text{ AB-ARC AC}) \\ ARC\text{ AB=146}^0 \\ \text{ARC AC=50}^0 \end{gathered}[/tex]
By substituing the values, we will have
[tex]\begin{gathered} \begin{equation*} \angle ADB=\frac{1}{2}(ARC\text{ AB-ARC AC}) \end{equation*} \\ \angle ADB=\frac{1}{2}(146^0-50^0) \\ \angle ADB=\frac{1}{2}(96^0) \\ \angle ADB=48^0 \end{gathered}[/tex]
Hence,
The value of angle ADB is
[tex]\Rightarrow\angle ADB=48^0[/tex]
Part B:
To figure out the value of arc angle CD, we will use the formula below
Hence,
The formula will be
[tex]\begin{gathered} \angle AEB=\frac{1}{2}(ARC\text{ AB+ARC CD}) \\ ARC\text{ AB=41}^0 \\ \angle AEB=42^0 \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} \begin{equation*} \angle AEB=\frac{1}{2}(ARC\text{ AB+ARC CD}) \end{equation*} \\ 42^0=\frac{1}{2}(41^0+arc\text{ CD}) \\ cross\text{ multiply, we will have} \\ 84=41^0+arc\text{ CD} \\ arc\text{ CD=84}^0-41^0 \\ arc\text{ CD=43}^0 \end{gathered}[/tex]
Hence,
The value of arc CD is
[tex]\Rightarrow arc\text{ CD=43}^0[/tex]
