Question

What is the measure of

Answer 1

Given:

The measure of
`\widehat{ADB}` is 162°

We need to determine the measure of ∠EAB

Measure of ∠EAB:

Let us determine the measure of ∠EAB

We know that, "If a tangent and chord intersect at a point on a circle, then the measure of each angle formed is half the measure of its intercepted arc".

Applying the above theorem, we get;

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

Substituting
`\widehat{ADB}=162^(\circ)`, we get;

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

Dividing, we get;

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

Thus, the measure of ∠EAB is 81°