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I went to the library and found this problem in a math book, called "The Solvable and the Unsolvable".

Here is the problem.

Consider a quadrilateral. Its vertices are A,B,C,D.

A is at the top left and B is at the top right lower than A.

C and D are collinear. C is at the bottom right and D is at the bottom left. D is further than A to the left and C is further than B to the right.

Please see the diagram below and IGNORE the dots which are needed to show the locations of the vertices.

..............A

......................................B

.....D_________________________C

Angle ABC is 160 degrees.

Angle CAB is 10 degrees.

Angle ACB is 10 degrees.

Angle CAD is 30 degrees.

Angle ACD is 70 degrees.

Angle ADC is 80 degrees.

Find angle BDC.

Is it possible to do? If it is, how do you do it? Thanks.