The bisectors of angles A and B in triangle ABC intersect at point O1.

The bisectors of angles A and B in triangle ABC intersect at point O1. The bisectors of the outer angles at the vertices A and B intersect at the point o2. The angle AO1B is 110 degrees. Find AO2B

Consider the quadrilateral obtained by intersecting the bisectors of the outer corners of the triangle ABC, let us denote it O2 B O1 A. In this quadrangle, the sum of opposite angles is 180 degrees. The AO1B angle is 110 degrees. This means that the angle AO2B = 180 – 110 = 70 degrees.