Question 1086563
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Angle ADC = 89 degrees (given)
Angle ACD = 42 degrees (given)


Focus on triangle ADC. Two angles are given. 
The third angle, angle DAC, is unknown. 
We can use the idea that three angles of a triangle add to 180 degrees to find angle DAC.


(Angle DAC) + (Angle ADC) + (Angle ACD) = 180
(Angle DAC) + (89) + (42) = 180
(Angle DAC) + 131 = 180
(Angle DAC) + 131 - 131 = 180 - 131
Angle DAC = 49


The angle DAC is an inscribed angle that cuts off minor arc CD.
The inscribed angle DBC also cuts off minor arc CD.
Therefore, these two inscribed angles are congruent


angle DBC = angle DAC
angle DBC = 49


Answer: <font color=red>49 degrees</font>
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