In triangle CDE with angle E equal to 32, bisector СF is drawn, angle CFD = 72. Find angle D

The angle СFD is the outer angle of the triangle CEF at the vertex F which is equal to the sum of the two inner angles of the triangle CEF, which are not adjacent to it.

CFD = ECF + CEF.

Angle ECF = CFD – CEF = 72 – 32 = 40.

Since СF is the bisector of the DCE angle, the angle DСF = ECF = 40.

In a triangle CDF, the angle CDF = (180 – DCF – CFD) = (180 – 40 – 72) = 68.

Answer: The value of the angle D is 68.