In triangle ABC, angle A = 56 and angle B = 38. the bisectors of angles B and C intersect at point O. What is the angle BOC?

Let us determine through how many degrees it is possible to express the angle C of our triangle, when from the condition of the task we know that the other two are 56 ° and 38 °, respectively:
180 – 56 – 38 = 86.
Let us determine through what number of degrees it is possible to express the angle of the BOC of the new triangle, when from the condition of the task we know that it was formed by the intersection of the bisectors of angles C and B:
38: 2 = 19;
86: 2 = 43;
180 – 19 – 43 = 180 – 62 = 118.
Answer: The BOC angle under such conditions will be equal to 118 ° (c).