We will be using the Angle Addition Postulate in this problem.
This states that if c is on the interior
of <ABD, then m<ABC + m<CBD = m<ABD.
Since m<ABC is 4x + 2, m<CBD is 3x - 7, and m<AVD is 100,
our equation will be 4x + 2 + 3x - 7 = 100.
Solving from here, we first simplify the left side to get 7x - 5 = 100.
Now add 5 to both sides to get 7x = 105.
Dividing both sides by 7, we find that x = 15.
Now we can use the value of x to help us find m<ABC.
Since the m<ABC is 4x + 2, we can substitute a 5 in for x.
This gives us 4(15) + 2 or 60 + 2 which is 62.
So m<ABC is 62°