1. **State the problem:** We are given two angles formed by the intersection of two lines: one angle measures $(3x + 33)^\circ$ and the opposite angle measures $(4x + 8)^\circ$. We need to find the measure of angle $\angle ABC$. 2. **Important rule:** Vertical angles formed by two intersecting lines are equal. Therefore, the two given angles are equal: $$3x + 33 = 4x + 8$$ 3. **Solve for $x$:** $$3x + 33 = 4x + 8$$ $$3x + 33 - 3x = 4x + 8 - 3x$$ $$33 = x + 8$$ $$33 - 8 = x$$ $$x = 25$$ 4. **Find the measure of $\angle ABC$:** Since $\angle ABC$ corresponds to one of the vertical angles, substitute $x=25$ into either expression. Using $(3x + 33)^\circ$: $$3(25) + 33 = 75 + 33 = 108$$ 5. **Answer:** The measure of $\angle ABC$ is $108^\circ$. Thus, the correct choice is 108°.