Choose the point E so that the lines EA and ED both make an
angle of 40° with AD.
Since BC = AD, and angle ABC = angle EAD = 40° and
angle ACB = angle EDA = 40°, the triangles ABC and EAD
Hence AC = AB = EA = ED.
Since AC = AE, triangle ACE is isoceles,
which implies that the angles AEC and ACE must be equal.
Since angle BAC = 100° and angle DAE = 40°, we have
angle EAC = 60°, and so angles AEC and ACE must each equal 60°.
Triangle ACE is therefore equilateral.
It follow that EC = EA, and hence EC = ED, so triangle ECD is
Angle DEC = 100° + 60° = 160°, so angle DCE = 10°,
and angle BCD = 60° - 40° - 10° = 10°