Question

applying the angle formed by a tangent and chord theorem
the measure of $widehat{adb}$ is 162°. what is the measure of $angle eab$?

Explanation:

Step1: Recall the tangent - chord angle theorem

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

Step2: Identify the intercepted arc

The angle $\angle EAB$ is formed by the tangent $EF$ and the chord $AB$, and the intercepted arc is $\overset{\frown}{AB}$. The measure of the major - arc $\overset{\frown}{ADB}=162^{\circ}$, and the measure of the whole circle is $360^{\circ}$. So the measure of the minor - arc $\overset{\frown}{AB}=360^{\circ}- 162^{\circ}=198^{\circ}$.

Step3: Calculate the measure of $\angle EAB$

By the tangent - chord angle theorem, $\angle EAB=\frac{1}{2}\overset{\frown}{AB}$. Since $\overset{\frown}{AB} = 198^{\circ}$, then $\angle EAB=\frac{1}{2}\times198^{\circ}=81^{\circ}$.

Answer:

$81$