To find the measure of ∠DBC, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Since ∠ABD is 60 degrees and ∠ABC is 155 degrees, we can find the measure of ∠DBC by subtracting the sum of those angles from 180 degrees.
∠DBC = 180° - (60° + 155°) = 180° - 215° = -35°
However, angles cannot have negative measures, so -35° is not a valid answer.
Therefore, it is not possible to find the measure of ∠DBC with the given information.