The measure of angle ABC = ABD + DBC = 95 degrees.
Let's plug our values from the picture into our equation above.
95 = 2x + 23 + 9x - 5
Combine like terms
95 = 11x + 18
Subtract 18 from both sides
77 = 11x
Divide both sides by 11
7 = x
Angle ABD = 2x + 23 = 2(7) + 23 = 14 + 23 = 37 degrees.
Angle DBC = 9x - 5 = 9(7) - 5 = 63 - 5 = 58 degrees.