Question

Referring to the figure, find the unknown measure of ABC.

Answer 1

According to the Inscribed Angle Theorem, the measure of an angle inscribed in a circle equals half the arc that it intercepts.

Then:

`m\angle ABC=(1)/(2)m\overset{\frown}{AC}`

Since the measure of the arc AC is equal to 84º, then:

`m\angle ABC=(1)/(2)(84º)=42º`

Therefore, the answer is:

The measure of ABC is 42º.