Question

applying the angle formed by a tangent and chord theorem
the measure of \\(\overarc{adb}\\) is \\(162^\circ\\). what is the measure of \\(\angle eab\\)?

Explanation:

Step1: Recall the Angle - Tangent and Chord 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 \( AB\). The intercepted arc is \( \overset{\frown}{ADB}\).

Step3: Calculate the measure of \( \angle EAB\)

By the Angle - Tangent and Chord Theorem, \( m\angle EAB=\frac{1}{2}m\overset{\frown}{ADB}\). Given \( m\overset{\frown}{ADB} = 162^{\circ}\), then \( m\angle EAB=\frac{1}{2}\times162^{\circ}\).

$$m\angle EAB = 81^{\circ}$$

Answer:

\(81\)