Answer: [tex]\angle{DBC} = 95[/tex]
We know that [tex]\angle ABC[/tex] is equal to 60 degrees (because of angle ABD) added to DBC, and it together gives 155 degrees. So we can make equation, where x is measure of DBC:
x + 60 = 155
x + 60 = 155 |(-60)
x + 60 - 60 = 155 - 60
x = 95
So the angle DBC is equal to 95 degrees. Hope this helps!