In a rectangle, the diagonal divides the angle by a ratio of 2: 7 Find the angle between the diagonals.

In the rectangle ABCD O is the point of intersection of the diagonals. ∟А = 90˚.
∟DAO: ∟BAO = 2: 7
Let us denote the coefficient of proportionality through x˚, then ∟DAO = 2х˚,
∟ВАО = 7х˚.
2x + 7x = 90
9x = 90
x = 10
∟DAO = 20˚, ∟BAO = 70˚
Consider ∆BAO, by the property of the diagonals of the rectangle AO = BO, Then
∟ВАО = ∟ABO = 70˚
The sum of the angles of a triangle is 180˚:
∟А0В = 180˚ – 2 * 70˚ = 40˚.
Answer. The angle between the diagonals is 40˚.