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The problem asks to determine the type of triangle and the sizes of the angles \( \alpha \) and \( \beta \), based on the provided diagram.

### Step-by-Step Solution:

1. **Identify Known Angles:**
   - From the diagram, we know that the exterior angle at \( B \) is \( 142^\circ \).

2. **Use of Exterior Angle Theorem:**
   The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In this case, the exterior angle \( 142^\circ \) is equal to the sum of \( \alpha \) and \( \beta \):
   \[
   \alpha + \beta = 142^\circ
   \]

3. **Determine Third Angle:**
   Since the sum of all angles in any triangle is \( 180^\circ \), the angle at \( C \) is given by:
   \[
   \angle C = 180^\circ - 142^\circ = 38^\circ
   \]

4. **Solve for \( \alpha \) and \( \beta \):**
   Now that we know the angle at \( C \), we can use it in the triangle \( ABC \). The sum of the interior angles of a triangle is also \( 180^\circ \), so we have:
   \[
   \alpha + \beta + 38^\circ = 180^\circ
   \]
   Substituting the value \( \alpha + \beta = 142^\circ \) into this equation:
   \[
   142^\circ + 38^\circ = 180^\circ
   \]
   This equation confirms that our values are consistent.

Thus, the triangle \( ABC \) is **scalene** (since all angles are different), and the angles are as follows:
- \( \alpha + \beta = 142^\circ \)
- \( \angle C = 38^\circ \)

Would you like further details on how to handle these types of geometry problems?

### Related Questions:
1. How can you calculate the length of the sides of this triangle if given?
2. What is the exterior angle theorem in more detail?
3. Can the type of triangle change if one of the angles is altered?
4. How can you apply trigonometry to find the side lengths given angles and one side?
5. How do we classify triangles based on their angles?

**Tip:** Always remember that the sum of the angles in any triangle must be \( 180^\circ \), which is helpful for finding unknown angles.

Bestimme die Dreiecksart und die Größe der Winkel α und β?

This problem involves determining the type of triangle and calculating the unknown angles α and β based on the given exterior angle and the sum of the triangle's interior angles. This exercise is perfect for students in Grades 7-9 and covers key geometry concepts such as the exterior angle theorem.

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