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An angle formed by a chord and a tangent line is half the measure of the intercepted arc.

 The intercepted arc is ADB, which is given as 162 degrees.

Angle EAB = 1/2 of 162

The answer is 81 degrees.

Answer:

∠EAB = 81°

Step-by-step explanation:

Given : [tex]\widehat{ADB} =162^{\circ}[/tex]

            Tangent = EF

            Chord = AB

To Find: ∠EAB

Solution :

We will use Tangent-Chord Angle Theorem

Tangent-Chord Angle Theorem :  An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc

Angle formed by a chord and a tangent that intersect on a circle =∠EAB

Intercepted arc  =  [tex]\widehat{ADB} =162^{\circ}[/tex]

So, by theorem

[tex]\angle {EAB} = \frac{1}{2}\widehat{ADB}[/tex]

[tex]\angle {EAB} = \frac{1}{2}\times 162^{\circ}[/tex]

[tex]\angle {EAB} = 81^{\circ}[/tex]

Hence the measure of ∠EAB is 81°

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