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;

$\angle EAB=\frac{1}{2} m(\widehat{ADB})$

Substituting $\widehat{ADB}=162^{\circ}$, we get;

$\angle EAB=\frac{1}{2}\times 162^{\circ}$

Dividing, we get;

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

Thus, the measure of ∠EAB is 81°