Exterior angle property of triangle by komal

To show that that exterior angle equals
 the sum of the opposite interior angles.

Z = X + Y

Slide = 11 (slider from 5 to 11, step 0.1)
A = (4.7, 8.88)
B = (5, 3)
C = (11, 3)
t1, c, a_1, b = Polygon(A, B, C)
D = (13, 3)
f = Ray(B, D)
α = Angle(C, B, A)
Z = Angle(D, C, A)
F = (5, 1)
G: (Slide, 1)
u = Vector(F, G)
A' = Translate(A, u)
B' = Translate(B, u)
C' = Translate(C, u)
t1', c', a', b' = Polygon(A', B', C')
H = Midpoint(A, C)
Rotate = 3.141592653589793 rad (slider from 0° to 180°, step 10°)
A'_1 = Rotate(A, (-Rotate), H)
B'_1 = Rotate(B, (-Rotate), H)
C'_1 = Rotate(C, (-Rotate), H)
t1'_1, c'_1, a'_1, b'_1 = Polygon(A'_1, B'_1, C'_1)
X = Angle(B'_1, A'_1, C'_1)
δ = Angle(B, A, C)
ε = Angle(B', A', C')
ζ, Y, θ = InteriorAngles(t1')
text1: "" + Z + "=" + X + "+" + Y + ""