Question

In a rhombus ABCD, m∠A = 31°. Point O is a point of intersection of diagonals. Find the measures of the angles of triangle ΔBOC.

find find I know

Answer 1

∠BOC = 90 degrees, ∠OCB = 15.5 degrees, ∠OBC = 74.5 degrees

Answer 2

check the picture below.

keeping in mind that the diagonals in a rhombus always meet at right-angles, thus all angles at point O are all right-angles.

now, notice that the AC angle bisector, cuts the angle at A in two equal halves, and if you look at the triangle BOC, there is a 15.5° angle, and a right-angle, and well, you already know what the last one is.