Angle Sum Identities
Author: Scott Farrar

Resize angles α and β to any measure such that α+β < π/2

Buttons at the bottom allow you to "Play" the construction.

1) Find expressions for the missing angles.
2) Find expressions for the sides of the rectangle.

r cosθ

r sinθ

A = (0, -3.2)
B = (1.4000000000000001, -3.2)
a = Ray(A, B)
changealpha = (1.0277530675194035, -2.7249025542108347)
α = Angle(B, A, changealpha)
b = Ray(A, changealpha)
changebeta = Point(Circle[A, 1])
c = Segment(A, changebeta)
β = Angle(changealpha, A, changebeta)
d = OrthogonalLine(changebeta, b)
E = Intersect(b, d)
δ = Angle(changebeta, E, A)
e = OrthogonalLine(E, a)
H = Intersect(a, e)
ζ = Angle(E, H, A)
g = OrthogonalLine(changebeta, e)
G = Intersect(e, g)
η = Angle(changebeta, G, E)
f = OrthogonalLine(A, g)
F = Intersect(f, g)
ε = Angle(A, F, changebeta)
m = Segment(A, H)
l = Segment(F, G)
poly1, h, a_1, e_1 = Polygon(A, E, H)
poly2, e_2, a_2, d_1 = Polygon(A, changebeta, E)
poly3, a_3, f_1, d_2 = Polygon(F, changebeta, A)
poly4, e_3, d_3, g_1 = Polygon(changebeta, G, E)
γ = Angle(F, changebeta, A)
θ_1 = Angle(G, E, changebeta)
ι = Angle(A, E, H)
C = (1.2000000000000002, -2.0500000000000003)
D = (1.3, -1.9500000000000002)
k = Circle(C, D)
i = Line(C, D)
I = Point(k)
J = Intersect(k, i, 2)
poly5, d_4, j, r = Polygon(J, I, D)
θ = Angle(I, J, D)
λ = Angle(D, I, J)