Question

Find the measure of ABC. Show work.

Answer 1

The measure of angle ∠ ABC is 96°.

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 = (1)/(2)* (center\ angle)\\`

On substituting the given values we get

∴
`m\angle ABC = (1)/(2)* 192\\m\angle ABC = 96\°`

Therefore, the measure of angle ∠ ABC is 96°