1. **State the problem:** We need to find the size of angle $q$ in the given hexagon-like shape and identify the angle fact used. 2. **Identify the angle fact:** The problem shows angles $120^\circ$, $60^\circ$, and $120^\circ$ around a point with angle $q$. The key angle fact here is that angles on a straight line sum to $180^\circ$. 3. **Apply the angle fact:** Since $q$ and the adjacent $120^\circ$ angle form a straight line, their sum is: $$q + 120^\circ = 180^\circ$$ 4. **Solve for $q$:** $$q = 180^\circ - 120^\circ$$ $$q = 60^\circ$$ 5. **Conclusion:** The size of angle $q$ is $60^\circ$. **Angle fact used:** Angles on a straight line sum to $180^\circ$.