Inerior Angles of Δ CBD

∠ CDA =∠DBC +∠BCD

The exterior angle theorem says that the size of an exterior 
angle at a vertex of a triangle equals the sum of the sizes 
of the interior angles at the other two vertices of the triangle.

Note: In order to see the effect, please click any point viz, A,
B,C and move it up or down or sideways. This changes the position 
position of vertices which produces different angles.

Use of slider may elongate the segments but the 
above very basic function has much to offer.

Author - Tharanath
Copyright - CC BY SA 4.0

A = (5.544731510331349, -6.2890913730117415)
B = (-6.426970495054801, -6.371723308520716)
a = Segment(A, B)
C = (-3.4230754441300344, 2.742771345410067)
b = Segment(B, C)
D = Point(a)
c = Segment(C, D)
α = Angle(B, C, D)
β = Angle(C, D, B)
γ = Angle(D, B, C)
δ = Angle(A, D, C)
text2: "∠DBC =" + γ + ""
text3: "∠BCD =" + α + ""
text4: "∠CDA = " + γ + " + " + α + ""
text5: "∴ ∠CDA = " + δ + ""