1. **Problem statement:** Given two lines and a ray intersecting to form five angles numbered 1 through 5, with $\angle 4 = 55^\circ$, find the measure of $\angle 2$. 2. **Understanding the setup:** The problem states $\angle 4 = 55^\circ$ and the diagram shows $\angle 4$ as a right angle (90°). This suggests a possible inconsistency, but we will proceed with the given $\angle 4 = 55^\circ$. 3. **Key fact:** Vertical angles are equal, and angles on a straight line sum to 180°. 4. **Identify relationships:** - $\angle 4$ and $\angle 5$ are adjacent and form a straight line, so: $$\angle 4 + \angle 5 = 180^\circ$$ - Substitute $\angle 4 = 55^\circ$: $$55^\circ + \angle 5 = 180^\circ$$ 5. **Solve for $\angle 5$:** $$\angle 5 = 180^\circ - 55^\circ = 125^\circ$$ 6. **Vertical angles:** $\angle 2$ and $\angle 5$ are vertical angles, so: $$\angle 2 = \angle 5 = 125^\circ$$ 7. **Final answer:** $\angle 2 = 125^\circ$. **Answer: B 125°**