1. **State the problem:** We need to find the size of angle $y$ adjacent to a $20^\circ$ angle on a straight line. 2. **Recall the rule:** Angles on a straight line add up to $180^\circ$. 3. **Set up the equation:** Since $y$ and $20^\circ$ are adjacent angles on a straight line, we have $$y + 20^\circ = 180^\circ$$ 4. **Solve for $y$:** $$y = 180^\circ - 20^\circ = 160^\circ$$ 5. **Conclusion:** The size of angle $y$ is $160^\circ$.