DB is longer
Work Step by Step
Since CAB is 80 degrees, this means that angle BAD is 40 degrees. In addition, CAD is equal to 40 degrees using the same logic. This means that DA is an angle bisector. Thus, if the line segment CB was perpendicular to DA, DB would be the same length as CD. However, since it is at an angle where BDA is greater that ADC, this means that DB is longer.