In triangle ABC, angle A is 27 °, angle B is 92 °. AD, BE and CF are bisseetrices intersecting at point O. Find the angle AOF.

1) Let’s represent the task using the figure

∟А = 27о, ∟В = 92о, AD, BE and CF – bisectors in ∆ABС, which divide the angles in half; О is the point of intersection of the bisectors.

2) Find ∟ AOB:

180o – (27o + 92o) / 2 = 180o – 59.5o = 120.5o.

3) Since OF is also a bisector for ∆AOB, then we find ∟AOF:

∟AOF = ∟АОВ: 2 = 120.5о: 2 = 60.25о.

Answer: ∟AOF = 60.25о.