1. **Problem statement:** Establish the correspondence between angles $\alpha$ and $\beta$ in a parallelogram. 2. **Recall the property:** In a parallelogram, adjacent angles are supplementary, meaning their sum is $180^\circ$. 3. **Apply the property:** For each given $\alpha$, calculate $\beta$ as $$\beta = 180^\circ - \alpha$$ 4. **Calculate for each case:** - For $\alpha = 30^\circ$, $\beta = 180^\circ - 30^\circ = 150^\circ$ (matches d) - For $\alpha = 40^\circ$, $\beta = 180^\circ - 40^\circ = 140^\circ$ (matches a) - For $\alpha = 50^\circ$, $\beta = 180^\circ - 50^\circ = 130^\circ$ (matches c) 5. **Final matching:** - $\alpha=30^\circ \to \beta=150^\circ$ (d) - $\alpha=40^\circ \to \beta=140^\circ$ (a) - $\alpha=50^\circ \to \beta=130^\circ$ (c)