Fold a piece of paper on the long diagonal.
Then fold the base up to form angle α.
Find angle β.

(this is scaled to American Letter 8.5 : 11)

A = (-12, 1)
B = (-11.956875276023219, 2.7870176757227694)
C = (-1, 8.5)
D = (-1, 1)
poly1, a, b, c, d = Polygon(A, B, C, D)
E = Point(b)
F = Point(d)
e = Segment(E, F)
poly2, e_1, c_1, d_1, f = Polygon(E, C, D, F)
E' = Mirror(E, e)
C' = Mirror(C, e)
D' = Mirror(D, e)
F' = Mirror(F, e)
poly2', e', c', d', f' = Polygon(E', C', D', F')
poly3, b_1, e_2, f_1, a_1 = Polygon(B, E, F, A)
α = Angle(A, F, D')
G = Intersect(b, c')
β = Angle(B, G, C')