exterior angle property of a triangle

We can see a triangle ABC in blue color. We can also see that line AC is extended to D. Angle BAC = α, angle ABC = β and angle BCD = У. Points A, B, and C are free points. Move these three points and see how the shape of the triangle and angles gets changed.
Questions to think about 1. Move the points A, B and C and calculate the value of (α+β). What do we observe? 2. Is it possible to get α+β ≠ У? 3. Let’s figure out how we can get the relation α+β=У