Here is the sample solution.
The answer assumes that the vertex of angle B is at the center of the circle. There is nothing in the statement of the question that stipulates this. In point of fact, the angle can change depending upon exactly where in the circle that vertex is. Drag that vertex in the diagram below.
A major MAJOR point in any Geometry course is, and must be, that care must be taken about making assumptions based on appearance. Just because the vertex looks like it could be the center does not mean it is.