In triangle ABC, the bisector of the outer angle adjacent to the angle B (BF) is drawn.

In triangle ABC, the bisector of the outer angle adjacent to the angle B (BF) is drawn. Prove that BF || AC if angles A = 50 and B = 80.

Determine the value of the external angle DВC.

Angles ABC and DBC are adjacent, the sum of which is 180, then the angle DBC = 180 – ABC = 180 – 80 = 100.

Current as BF is the bisector of the outer angle, then the angle is DBF = CBF = DВС / 2 = 100/2 = 50.

Angle DBF = BAC = 50, and since these are the corresponding angles at the intersection of parallel straight lines BF and AC of the secant AD, then the AC side is parallel to the bisector BF, which was required to prove.