Question

The measure of ADB is 162 . what is the measure of EAB?

Answer 1

∠EAB = 81°

Explanation:

Given :
`\widehat{ADB} =162^(\circ)`

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 =
`\widehat{ADB} =162^(\circ)`

So, by theorem

`\angle {EAB} = (1)/(2)\widehat{ADB}`

`\angle {EAB} = (1)/(2)* 162^(\circ)`

`\angle {EAB} = 81^(\circ)`

Hence the measure of ∠EAB is 81°

Answer 2

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.