TITLE: How to find missing angles in a quadrilateral
QUESTION [6 upvotes]: I have a quadrilateral ABCD, with diagonals AC and BD.
Given are four angles: ∠DAC = 20°, ∠CAB = 60°, ∠ABD = 50°, and ∠DBC = 30°.

Those are the red angles in the above image.
I need to fill in all the other angles.  Most are trivial – the angles in blue – but how do I find ∠BDC and ∠ACD?  Their sum is 110, obviously, but I can't figure out how to find the individual angles.
Edit:  Note that the red angles are examples; I'm looking for a general solution given any values for these angles that form a convex quadrilateral.  (They do if ∠DAC + ∠CAB + ∠ABD < 180° and ∠CAB + ∠ABD + ∠DBC < 180; in that case you can draw triangles ABD and ABC and then quadrilateral ABCD.)

REPLY [7 votes]: I have four different and one general solution to this problem, I hope it will help you.