Question

the measure of $overparen{adb}$ is 162°. what is the measure of $angle eab$?

Explanation:

Step1: Recall the tangent - secant angle relationship

The measure of an angle formed by a tangent and a secant is half the measure of the intercepted arc. Here, $\angle EAB$ is an angle formed by the tangent $EF$ and the secant $AB$. The intercepted arc is $\overset{\frown}{ADB}$.

Step2: Apply the formula

The formula for the measure of the angle formed by a tangent and a secant is $\angle EAB=\frac{1}{2}\text{ measure of }\overset{\frown}{ADB}$. Given that the measure of $\overset{\frown}{ADB} = 162^{\circ}$, then $\angle EAB=\frac{1}{2}\times162^{\circ}$.

Answer:

$81^{\circ}$