When a ray bisects an angle, it divides the angle into two equal parts. In this case, ray BC bisects angle ABD, which measures 112 degrees. To find the measures of angles ABC and CBD, we divide the measure of angle ABD by 2. Therefore, m/ABC = m/CBD = 112 degrees / 2 = 56 degrees. However, since the question states that m/ABC is 34 degrees and m/CBD is 78 degrees, it indicates that there might be an error in the provided values or the interpretation of the diagram. The correct interpretation should yield equal angles from the bisection.