Given
The measure of the arc AC is [tex]m \widehat{A C}=82^{\circ}[/tex]
The measure of the angle ABC is [tex]m \widehat{A BC}=x[/tex]
We need to determine the value of x.
Value of x:
The inscribed angle theorem states that, "the measure of an inscribed angle is half the measure of the intercepted arc".
Applying this theorem, we have;
[tex]m \angle A B C=\frac{1}{2} m \widehat{A C}[/tex]
Substituting the values, we get;
[tex]x=\frac{1}{2}(82^{\circ})[/tex]
[tex]x=41^{\circ}[/tex]
Thus, the value of x is 41°
Therefore, the measure of angle ABC is 41°
