We are given the angle $CBC = 100$ and the angle $AAC = 4$. We need to find the measure of angle $ABC$.

1. Problem Description

We are given the angle $CBC = 100$ and the angle $AAC = 4$. We need to find the measure of angle $ABC$.

2. Solution Steps

We are given the measures of angles $CBC$ and $AAC$. Note that the points A, B, and C form triangle $ABC$. Therefore, the sum of the angles in triangle $ABC$ must be $180$ degrees. That is:

$ABC + BCA + CAB = 180$

Also, notice that $CBC$ refers to angle $B$ of the triangle and $AAC$ refers to the angle $A$ of the triangle.

So, $ABC = 100$ and $BAC = 4$. We need to find the measure of $ABC$.

Substituting these values into the equation for the sum of the angles in the triangle, we get:

$ABC + BCA + BAC = 180$

$100 + BCA + 4 = 180$

$BCA + 104 = 180$

$BCA = 180 - 104$

$BCA = 76$

The problem statement mentions that $CBC=100$, this is confusing as the point C appears twice. I will assume that it refers to the angle $ABC=100$. The second given piece of information is that $AAC=4$, this is confusing as well, I will assume it is meant to be angle $BAC=4$.

The sum of the angles of triangle $ABC$ is $180$, therefore:

$ABC + BAC + BCA = 180$

Substituting the given values into the equation we get:

$100 + 4 + BCA = 180$

$104 + BCA = 180$

$BCA = 180 - 104 = 76$

The question asks for the measure of angle $ABC$, which we are given in the problem statement. We know that the angle $CBC = ABC = 100$.

3. Final Answer

$ABC=100$