Find the measure of $angle ABC$ if arc $oversetfrown{AC}$ is 120 degrees

To find the measure of $\angle ABC$ given that the arc $\overset\frown{AC}$ is 120 degrees, we use the Inscribed Angle Theorem. The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Therefore,

$ \angle ABC = \frac{1}{2} \times \overset\frown{AC} $

Substitute the measure of the arc:

$ \angle ABC = \frac{1}{2} \times 120^\circ $

The measure of $\angle ABC$ is:

$ \angle ABC = 60^\circ $

To find the measure of $angle ABC$ given that the arc $oversetfrown{AC}$ is 120 degrees, use the Inscribed Angle Theorem, which states:

$ angle ABC = frac{1}{2} imes oversetfrown{AC} $

Thus,

$ angle ABC = frac{1}{2} imes 120^circ = 60^circ $

Using the Inscribed Angle Theorem:

$ angle ABC = frac{1}{2} imes oversetfrown{AC} $

Substitute the value:

$ angle ABC = frac{1}{2} imes 120^circ = 60^circ $

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