In rhombus ABCD, the diagonals intersect at point O, angle BAC = 32 degrees. Find the corners of the triangle BOC.

Consider triangles BAO and BCO. They are equal, according to the third criterion: AB = BC (the sides in the rhombus are equal to each other), BO-common side, AO = OC (the diagonals in the rhombus are halved by the point of intersection). It follows from the equality of the triangles that the angle BAO = angle BCO = 32.
Consider a triangle BCO. It is rectangular because the diagonals in the rhombus intersect at right angles. Therefore, the angle BOC = 90
Let’s calculate the angle OBC: 180-90-32 = 58
Answer: angle BCO = 32, angle BOC = 90, angle OBC = 58.