Angle BAC = 15 degrees, since BAC and DCA are alternate interior angles, so they are congruent to one another. This works because AB is parallel to CD.
Ignore point D. Focus on triangle BAC only. Two angles are known: A = 15, B = 153. Solve for angle C
A+B+C = 180
15+153+C = 180
C+168 = 180
C = 180-168
C = 12
For triangle ABC (ignore point D) the angle C is 12 degrees. If D is involved in the diagram, angle BCA is 12 degrees.
