Question

50 points to whoever gets it correct

Answer 1

Here AC = 82⁰

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

Thus angle ABC = 1/2 × 82 = 41 ⁰

Answer 2

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=(1)/(2) m \widehat{A C}`

Substituting the values, we get;

`x=(1)/(2)(82^(\circ))`

`x=41^(\circ)`

Thus, the value of x is 41°

Therefore, the measure of angle ABC is 41°