Question

Tangent line AD and chord AC intersect at point A. If the measure of ABC is 220°, what is the measure of Angle CAD?

Answer 1

Let's imagine a point E in the line DA and at the left of point A.

From the formula to find the angle between a tangent and a chord:

`m\angle CAE=(1)/(2)m\angle CBA`

The measure of angle ABC is given: 220°. Then:

`\begin{gathered} m\angle CAE=(1)/(2)\cdot220^o \\ m\angle CAE=110^o \end{gathered}`

Now, from the figure, we can see that angles CAE and CAD form an angle of 180°. Then:

`m\angle CAD+m\angle CAE=180^o`

Replacing values and solving:

`\begin{gathered} m\angle CAD+110^o=180^o \\ m\angle CAD=180^o-110^o \\ m\angle CAD=70^o \end{gathered}`

Then, finally, the measure of angle CAD is 70°.