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The image presents a parallelogram \( ABCD \), where we are asked to calculate \( \alpha + \beta \) given certain angles. Here's a breakdown of the problem:

1. The angle in the upper-right corner is given as \( 144^\circ \).
2. In the lower-left corner, there is an angle marked as \( 3\beta \).
3. The upper-left corner angle is marked as \( 2\alpha \).

### Key Properties of a Parallelogram:
- Opposite angles of a parallelogram are equal.
- Adjacent angles of a parallelogram are supplementary, meaning their sum is \( 180^\circ \).

### Solving the Problem:

1. **First, relate \( 2\alpha \) and \( 144^\circ \):**  
   Since they are adjacent angles in the parallelogram, they must sum up to \( 180^\circ \):
   \[
   2\alpha + 144^\circ = 180^\circ
   \]
   Solving for \( \alpha \):
   \[
   2\alpha = 180^\circ - 144^\circ = 36^\circ
   \]
   \[
   \alpha = \frac{36^\circ}{2} = 18^\circ
   \]

2. **Next, relate \( 3\beta \) and \( 144^\circ \):**  
   These angles are opposite angles, and in a parallelogram, opposite angles are equal. Therefore:
   \[
   3\beta = 144^\circ
   \]
   Solving for \( \beta \):
   \[
   \beta = \frac{144^\circ}{3} = 48^\circ
   \]

### Final Calculation:
Now that we have both \( \alpha \) and \( \beta \), we can calculate \( \alpha + \beta \):
\[
\alpha + \beta = 18^\circ + 48^\circ = 66^\circ
\]

Thus, \( \alpha + \beta = 66^\circ \).

---

Would you like further details or have any other questions?

### Related Questions:
1. How do the properties of parallelograms help in solving angle problems?
2. What other shapes have supplementary adjacent angles?
3. Can you solve a parallelogram problem with unknown side lengths given angles?
4. How would this change if the parallelogram was a rectangle?
5. Why are opposite angles equal in parallelograms?

### Tip:
When working with parallelograms, always remember that adjacent angles are supplementary, and opposite angles are equal. This helps in quickly setting up equations.

Si ABCD es un paralelogramo, calcula α + β.

This problem involves calculating the sum of two unknown angles (α + β) in a parallelogram using the properties of supplementary and opposite angles. The solution uses basic geometry and algebra suitable for students in Grades 8-10.

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