To solve for the angle $\alpha$ in this isosceles triangle (since $AB = AC$), let's use the information provided:

1. $\triangle ABC$ is isosceles, so angles $\angle B$ and $\angle C$ should be related to each other.
2. The interior angles of any triangle must sum to 180°.

Given:

• $\angle A = 33^\circ$
• $\angle B = 50^\circ$
• $\angle C = 56^\circ$

Step 1: Confirm the sum of angles

We first check the sum of the interior angles of $\triangle ABC$:

$33^\circ + 50^\circ + 56^\circ = 139^\circ$

This means the remaining $180^\circ - 139^\circ = 41^\circ$ would account for any angle discrepancies or further divisions inside the triangle.

Step 2: Use geometrical properties

Since $AB = AC$, the triangle is isosceles. The two blue diagonals inside the triangle divide it into smaller triangles. One of these smaller triangles gives $\alpha$, the angle we need to find. Using the marked values of $235^\circ$ and $175^\circ$ around $\alpha$, we apply external or supplementary angle properties, if relevant.

I'll proceed with the full calculation of $\alpha$.The remaining angle discrepancy for the triangle is $41^\circ$. This suggests that further details, such as relationships between the internal diagonals or supplementary angles (e.g., using the external angles of $235^\circ$ and $175^\circ$), need to be applied to find $\alpha$.

Do you want more detailed steps on how to apply the internal diagonals or angles to solve for $\alpha$, or any additional questions regarding this geometry problem?

Here are some related questions to explore further:

1. How are supplementary angles used in an isosceles triangle?
2. What is the role of the exterior angles in determining the interior angles?
3. How can diagonals inside a triangle help find unknown angles?
4. Can we apply any symmetry properties to simplify the calculation of $\alpha$?
5. How do the base angles relate to the vertex angle in isosceles triangles?

Tip: When working with isosceles triangles, always leverage the property that two sides are equal, which simplifies angle relationships.