Question

50 points to whoever gets it correct

Answer 1

Given

The measure of the arc AC is $m \widehat{A C}=82^{\circ}$

The measure of the angle ABC is $m \widehat{A BC}=x$

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;

$m \angle A B C=\frac{1}{2} m \widehat{A C}$

Substituting the values, we get;

$x=\frac{1}{2}(82^{\circ})$

$x=41^{\circ}$

Thus, the value of x is 41°

Therefore, the measure of angle ABC is 41°

Answer 2

Answer:

Here AC = 82⁰

The angle ABC will be half the length of arc AC .

Thus angle ABC = 1/2 × 82 = 41 ⁰