The arc size AB is 54 degrees. Find the degree measure of the inscribed angle ACB

Given:

arc AB = 54 °,

To find:

inscribed angle ACB.

Decision:

Let’s use the inscribed angle property: the inscribed angle is equal to half of the arc on which it rests. Since the inscribed angle ABC rests on the arc AB, therefore, the inscribed angle ABC is equal to half of this arc.

We get:

angle ACB = arc AB: 2,

angle АСВ = 54 °: 2,

angle АСВ = 27 °.

Answer: angle ACB = 27 °.