Notice that point D is inside the angle ABC, so it divides it in two sections:
One is ABD which equals 3 x - 2, and the other section is DBC which equals x + 17.
We are aske to find each os this angles knowing that the original one is 31.
so we write that the addition of the two newly formed angles should equal the measure of the original angle (310> We do that via the formula:
ABD + DBC = 31
3 x - 2 + x + 17 = 31
by combining like terms we get:
4 x + 15 = 31
4 x = 31 - 15
4 x = 16
x = 16/4
x = 4
So we know the measure of "x", and with this we can find the measure of ABD and DBC:
ABD = 3 x - 2 = 3 (4) -2 = 12 - 2 = 10
DBC = x + 17 = 4 + 17 = 21
So, the measure of ABD = 10 , the measure of DBC = 21