1. **State the problem:** We are given two adjacent angles formed by a ray originating from a point on line segment AB. The angles are labeled $2y + 60$ and $y$. We need to find the value of $y$. 2. **Understand the relationship:** Adjacent angles formed by a ray on a straight line are supplementary, meaning their sum is $180^\circ$. 3. **Set up the equation:** $$ (2y + 60) + y = 180 $$ 4. **Combine like terms:** $$ 2y + 60 + y = 180 \\ 3y + 60 = 180 $$ 5. **Isolate $y$:** $$ 3y + \cancel{60} - \cancel{60} = 180 - 60 \\ 3y = 120 $$ 6. **Solve for $y$:** $$ \frac{3y}{\cancel{3}} = \frac{120}{\cancel{3}} \\ y = 40 $$ 7. **Answer:** The value of $y$ is $40^\circ$.