Given:
The measure of [tex]\widehat{ADB}[/tex] 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;
[tex]\angle EAB=\frac{1}{2} m(\widehat{ADB})[/tex]
Substituting [tex]\widehat{ADB}=162^{\circ}[/tex], we get;
[tex]\angle EAB=\frac{1}{2}\times 162^{\circ}[/tex]
Dividing, we get;
[tex]\angle EAB=81^{\circ}[/tex]
Thus, the measure of ∠EAB is 81°
