Find m<ABC if line BD is an angle bisector of angle ABC and m<ABC = 4x - 5 degrees and angle b is x + 6 degrees

ABC = 4x - 5 = 2b = 2(x + 6),

4x - 5 = 2(x + 6),
4x - 5 = 2x + 12,
4x - 2x = 12 + 5,
2x = 17,
x = 17/2,

ABC = 4X - 5 = 4*17/2 - 5 = 34 - 5 = 29
deg.

To find the measure of angle ABC, we need to set up an equation using the fact that angle BD is an angle bisector.

We know that angle BDC is divided into two congruent parts by the angle bisector BD. So, we have:

m<ABC = m<ABD + m<DBC

In this case, we are given that m<ABC is equal to 4x - 5 degrees and m<DBC is equal to x + 6 degrees. We can substitute these values into the equation:

4x - 5 = x + 6

Now we can solve for x. Subtracting x from both sides gives:

3x - 5 = 6

Adding 5 to both sides gives:

3x = 11

Finally, dividing both sides by 3 gives:

x = 11/3

Now that we have the value of x, we can substitute it back into the original equation to find the measure of angle ABC:

m<ABC = 4x - 5
= 4(11/3) - 5
= 44/3 - 5
= 44/3 - 15/3
= 29/3

Therefore, the measure of angle ABC is 29/3 degrees.