To find the measure of ∠DBC, we can use the fact that the angles around point B must add up to 360°.
We know:
- ∠ABD = 60°
- ∠ABC = 155°
To find ∠DBC, we can first find the measure of ∠ABO using: \[ \text{Measure of angle around point B} = ∠ABD + ∠ABC + ∠DBC = 360° \]
Rearranging this gives: \[ ∠DBC = 360° - (∠ABD + ∠ABC) \]
Substituting the values we have: \[ ∠DBC = 360° - (60° + 155°) = 360° - 215° = 145° \]
It appears there was a miscalculation because none of the options provided matches this.
Alternatively, if you are interpreting the angles as parts of a straight line (and given the information):
Then consider the relation: \[ ∠ABC = ∠ABD + ∠DBC \]
Then we can rearrange to find: \[ ∠DBC = ∠ABC - ∠ABD = 155° - 60° = 95° \]
Thus, the correct measure of ∠DBC is C. 95°.