In rhombus ABCD, angle A = 31 degrees. The diagonals intersect point O. Find the angles of the triangle angle BOC.

To solve problems of this type, the main thing is to know this property of the diagonals of a rhombus. They intersect at right angles and are bisectors of the corners of the rhombus.
By condition, angle A = 31 °, angle A = angle C.
Consider a BOC right-angled triangle, the corners of which we need to find:
BOC angle = 90 ° (diagonals are perpendicular).
Angle ВСО = 31 ° / 2 = 15.5 ° (diagonals – bisectors).
CВO angle = 90 ° – 15.5 ° = 74.5 °.
Answer: The angles of the ВOC triangle have a degree measure: 15.5 °, 74.5 °, 90 °.