In triangle ABC, angle B is obtuse, continuation of heights AA1, BB1, CC1 intersect at point O

In triangle ABC, angle B is obtuse, continuation of heights AA1, BB1, CC1 intersect at point O, angle AOC = 60 degrees. Find the angle ABC.

Consider a quadrangle BA1OC1 formed by the continuation of the heights AA1, CC1, and BB1.

Angle BA1O = BC1O = 90, since AA1 and CC1 are the heights of triangle ABC.

The sum of the inner angles of the quadrilateral BA1OC1 is 360, then the angle A1BC1 = (360 – 90 – 90 – 60) = 120.

The sought angle ABC and the angle A1BC1 are the vertical angles whose degree measure is, then the angle ABC = A1BC1 = 120.

Answer: Angle ABC is 120.