The bisectors of angles B and C of triangle ABC intersect at point K.

The bisectors of angles B and C of triangle ABC intersect at point K. Find the angle BКС if the angle B = 40 degrees and the angle C = 80 degrees.

Consider the triangle BKC, which appears as a result of the intersection of the bisectors of the angles B and C of the triangle ABC. Two angles are known in the BKC triangle:
angle B = 40 ° / 2 = 20 °;
angle C = 80 ° / 2 = 40 °.
The sum of the angles of the triangle is 180 °, so we find the angle BKC.
angle BKC = 180 ° – (20 ° + 40 °) = 180 ° – 60 ° = 120 °
Answer: The BKC angle is 120 °.