We are given a circle with center B. Arc $AD$ measures $114^\circ$. We want to find the measure of angle $ACD$.

1. Problem Description

We are given a circle with center B. Arc $AD$ measures $114^\circ$. We want to find the measure of angle $ACD$.

2. Solution Steps

The inscribed angle theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. In this case, $\angle ACD$ is an inscribed angle that intercepts arc $AD$.

Inscribed Angle Theorem:

$m\angle ACD = \frac{1}{2} \cdot m \stackrel{\frown}{AD}$

We are given that $m \stackrel{\frown}{AD} = 114^\circ$.

Substituting this value into the formula, we get

$m\angle ACD = \frac{1}{2} \cdot 114^\circ = 57^\circ$

3. Final Answer

57