Answer
The measure of $\angle ABC$ in terms of $\beta$
$$\angle ABC=180^\circ-\beta$$
Work Step by Step
We know from the image that $\angle CBx=\beta$
Also, from the image, we get that $\angle ABC$ and $\angle CBx$ are supplementary angles, so they add up to 180 degrees.
Therefore, $$\angle ABC+\angle CBx=180^\circ$$
$$\angle ABC+\beta=180^\circ$$
$$\angle ABC=180^\circ-\beta$$
This is the measure of $\angle ABC$ in terms of $\beta$.