1. **State the problem:** Find the degree measure of the angle marked with an arc at the bottom of the figure, given that the angles are supplementary and some angles are labeled as $x=42^\circ$, $y=60^\circ$, and the bottom angle is composed of $60^\circ + 55^\circ$. 2. **Recall the definition of supplementary angles:** Two angles are supplementary if their measures add up to $180^\circ$. 3. **Analyze the given information:** The bottom angle is the sum of $60^\circ$ and $55^\circ$. 4. **Calculate the bottom angle:** $$ 60 + 55 = 115 $$ 5. **Conclusion:** The angle marked with an arc at the bottom of the figure measures $115^\circ$. **Final answer:** 115