If Triangle ADC is congruent to Triangle BDC, then the measure of angle BCD= what degrees?

Angle A = Angle B

56  - 3a =   8a + 1    rearrange as

56 -1  = 8a + 3a

55  = 11a

Dived both sides  by  11

5  =a

So angle  B  =8(5) + 1 =   41° 

We know that angle D  =107°

Therefore, angle C   = 180   - 107    - 41   =   32°