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The image shows two triangular shapes with angles labeled. The left triangle has angles labeled \(2\beta\), \( \beta\), and 100°, while the right triangle has angles labeled \(\alpha\), \(\beta\), and a small angle at the base.

Let's analyze and deduce the relationships between these angles:

### Left Triangle:
- The triangle has angles \(2\beta\), \(100^\circ\), and \(\beta\).
- We know the sum of angles in any triangle is \(180^\circ\), so we can write:
  \[
  2\beta + 100^\circ + \beta = 180^\circ
  \]
  Simplifying:
  \[
  3\beta + 100^\circ = 180^\circ
  \]
  \[
  3\beta = 80^\circ
  \]
  \[
  \beta = \frac{80^\circ}{3} \approx 26.67^\circ
  \]

### Right Triangle:
- The triangle has angles \(\alpha\), \(\beta\), and an unknown small angle.
- Using the value of \(\beta \approx 26.67^\circ\), we can explore this further if more details about the right triangle are provided (such as the angle \(\alpha\)).

Would you like to proceed with solving for \(\alpha\) or any other aspects of this diagram? Here are some follow-up questions that might help:

1. What is the relationship between \(\alpha\) and \(\beta\) in the right triangle?
2. Are the two triangles symmetrical or share a specific property?
3. Can we assume the small angle in the right triangle is related to the others?
4. Would you like a more detailed calculation for \(\beta\)?
5. Are there any other parts of this diagram you'd like to explore?

**Tip**: When solving for angles in geometric figures, always check whether there are any parallel lines or specific shapes like isosceles or equilateral triangles. This often helps in finding angle relationships easily.

The image shows two triangular shapes with angles labeled. The left triangle has angles labeled 2β, β, and 100°, while the right triangle has angles labeled α, β, and an unknown small angle.

Explore how to find unknown angles in two connected triangles, one with angles labeled 2β, β, and 100°, and the other with angles labeled α and β. This problem involves the sum of angles in triangles and the use of geometric relationships to solve for unknowns.

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