Question

Do number 4. not drawn to scale.i only care about the answers & the steps

Answer 1

You can identify that the angle CAB is an angle formed by the intersection of a Tangent and a Chord. The Tangent is DA.

By definition, the measure of an angle formed by the intersection on a Tangent and a Chord and whose vertex is on the circle, can be calculated dividing the Intercepted arc by 2. Therefore:

`m\angle CAB=(mAB)/(2)`

As you can notice, the exercise does not provide the measure of the Intercepted arc, but you know that:

`m\angle BAD=101\degree`

Analyzing the figure, you can conclude that the angle CAB and the angle BAD are Supplementary angles, this means that they add up to 180 degrees. Then you can set up the following equation in order to find the measure of the angle CAB:

`m\angle BAD+m\angle CAB=180\degree`

Subsituting the known measure and solving for the angle CAB, you get:

`\begin{gathered} 101\degree+m\angle CAB=180\degree \\ m\angle CAB=180\degree-101\degree \\ m\angle CAB=79\degree \end{gathered}`

Substitute the measure found into the equation

`m\angle CAB=(mAB)/(2)`

And solve for mAB:

`\begin{gathered} 79\degree=(mAB)/(2) \\ \\ (2)(79\degree)=mAB \\ mAB=158\degree \end{gathered}`

The answers are:

`\begin{gathered} m\angle CAB=79\degree \\ \\ mAB=158\degree \end{gathered}`