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

Tangent Line AD And Chord AC Intersect At Point A If The Measure Of ABC Is 220 What Is The Measure Of Angle CAD class=

Sagot :

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:

[tex]m\angle CAE=\frac{1}{2}m\angle CBA[/tex]

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

[tex]\begin{gathered} m\angle CAE=\frac{1}{2}\cdot220^o \\ m\angle CAE=110^o \end{gathered}[/tex]

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

[tex]m\angle CAD+m\angle CAE=180^o[/tex]

Replacing values and solving:

[tex]\begin{gathered} m\angle CAD+110^o=180^o \\ m\angle CAD=180^o-110^o \\ m\angle CAD=70^o \end{gathered}[/tex]

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

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