Question

Find the measure of ABC. Show work.

Answer 1

Answer:

The measure of angle ∠ ABC is 96°.

Step-by-step explanation:

Inscribed angle theorem:

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

Here,

central angle is 192°

∴ $m\angle ABC = \frac{1}{2}\times (center\ angle)$

On substituting the given values we get

∴ $m\angle ABC = \frac{1}{2}\times 192\\m\angle ABC = 96\°$

Therefore, the measure of angle ∠ ABC is 96°