We are asked to find the measure of angle $ABC$ in a circle, given that the measure of arc $AC$ is 55 degrees.

1. Problem Description

We are asked to find the measure of angle $ABC$ in a circle, given that the measure of arc $AC$ is 55 degrees.

2. Solution Steps

The measure of an inscribed angle is half the measure of its intercepted arc. In this case, angle $ABC$ is an inscribed angle that intercepts arc $AC$. Therefore, the measure of angle $ABC$ is half the measure of arc $AC$.

We are given that $m\stackrel{\frown}{AC} = 55^{\circ}$.

We use the inscribed angle theorem, which states:

$m\angle ABC = \frac{1}{2} m\stackrel{\frown}{AC}$

$m\angle ABC = \frac{1}{2} (55^{\circ})$

$m\angle ABC = 27.5^{\circ}$

3. Final Answer

27.5