In triangle abc, a bisector bd is drawn which intersects side ac at point d from point d a straight line df is drawn

In triangle abc, a bisector bd is drawn which intersects side ac at point d from point d a straight line df is drawn which intersects side bc at point f so that bf = fd find the angle abc if the angle bdf = 39 degrees.

Consider the resulting triangle BDF: BF = FD (by condition), so this is an isosceles triangle with base BD.

In an isosceles triangle, the angles at the base are equal, which means that the angle FBD is equal to the angle BDF = 39 °.

And since BD is a bisector, it means that the angle ABC is 39 ° * 2 = 78 °.

Answer: the angle ABC is 78 °.