From the vertex of the unfolded angle BDM, the bisector DE and the ray DC are drawn so that the angle

From the vertex of the unfolded angle BDM, the bisector DE and the ray DC are drawn so that the angle CDE = 19 °. What can be the degree measure of the angle BDC?

By convention, the BDM angle is unfolded, so its degree measure is 180. Since DE is the bisector of the BDM angle, and the bisector divides the angle into two equal parts, the EDM angle = EDB angle = 90. The degree measure of the desired angle will depend on where the CD side of the CDE is.
Case 1: CD side inside EDM corner.
BDC angle = EDB angle + CDE angle = 90 + 19 = 109 degrees.
Case 2: the side of the CD is inside the corner of the EDB.
Angle BDC = Angle EDB – Angle CDE = 90-19 = 71 degrees.
Answer: 109 degrees or 71 degrees.