The diagonals of the rectangle ABCD intersect at the point o find the value of the acute angle

The diagonals of the rectangle ABCD intersect at the point o find the value of the acute angle between the diagonals of the rectangle if the angle of the BAO is 30 degrees

The diagonals of the rectangle are equal and are halved at the point of their intersection. Then AO = ОD = OC = ОВ, which means that the triangles AOB, BOС, COD, AOD are isosceles.

In the triangle AOB, the angles at the base are AB = 30, then the angle AOB = 180 – 30 – 30 = 120.

The angle AOB and AOB are adjacent angles, the sum of which is 180, then the angle AOD = 180 – AOB = 180 – 120 = 60.

Answer: The acute angle between the diagonals is 60.