The sides BC and AD of a quadrilateral ABCD are parallel and the diagonals intersect in O. For this quadrilateral ∣CD∣=∣AO∣ and ∣BC∣=∣OD∣ hold. Furthermore CA is the angular bisector of angle BCD. Determine the size of angle ABC.[asy]
unitsize(1 cm);pair A, B, C, D, O;D = (0,0);
B = 3*dir(180 + 72);
C = 3*dir(180 + 72 + 36);
A = extension(D, D + (1,0), C, C + dir(180 - 36));
O = extension(A, C, B, D);draw(A--B--C--D--cycle);
draw(B--D);
draw(A--C);dot("A", A, N);
dot("B", B, SW);
dot("C", C, SE);
dot("D", D, N);
dot("O", O, E);
[/asy]Attention: the figure is not drawn to scale. parallelgeometryanglesdiagonals