Question

I need assistance with a geometry worksheet. Find missing information for both parts below?

Answer 1

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

`\begin{gathered} \angle ADB=(1)/(2)(ARC\text{ AB-ARC AC}) \\ ARC\text{ AB=146}^0 \\ \text{ARC AC=50}^0 \end{gathered}`

By substituing the values, we will have

`\begin{gathered} \begin{equation*} \angle ADB=(1)/(2)(ARC\text{ AB-ARC AC}) \end{equation*} \\ \angle ADB=(1)/(2)(146^0-50^0) \\ \angle ADB=(1)/(2)(96^0) \\ \angle ADB=48^0 \end{gathered}`

Hence,

The value of angle ADB is

`\Rightarrow\angle ADB=48^0`

Part B:

To figure out the value of arc angle CD, we will use the formula below

Hence,

The formula will be

`\begin{gathered} \angle AEB=(1)/(2)(ARC\text{ AB+ARC CD}) \\ ARC\text{ AB=41}^0 \\ \angle AEB=42^0 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} \begin{equation*} \angle AEB=(1)/(2)(ARC\text{ AB+ARC CD}) \end{equation*} \\ 42^0=(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}`

Hence,

The value of arc CD is

`\Rightarrow arc\text{ CD=43}^0`