1. **Stating the problem:** We have a parallelogram with angles labeled $\alpha$, $\beta$, $\gamma$, and one angle given as $108^\circ$. The side length at the bottom is $11$, the right side length is $6.3$, and the top side length is $a$. We need to find the values of $\alpha$, $\beta$, $\gamma$, and the length $a$. 2. **Properties of a parallelogram:** Opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$). Opposite sides are equal in length. 3. **Finding the angles:** Given one angle is $108^\circ$, its opposite angle is also $108^\circ$. Adjacent angles are supplementary, so $$\beta = 180^\circ - 108^\circ = 72^\circ.$$ Since $\alpha$ and $\gamma$ are opposite angles, they equal $\beta$, so $$\alpha = \gamma = 72^\circ.$$ 4. **Finding the side length $a$:** Opposite sides are equal in a parallelogram, so the top side length $a$ equals the bottom side length: $$a = 11.$$ 5. **Summary:** - $\alpha = 72^\circ$ - $\beta = 108^\circ$ - $\gamma = 72^\circ$ - $a = 11$ This completes the solution.