The diagonal of a rectangle divides its angle in a ratio of 4: 5 find the angle between the diagonals.

Let us determine what the smaller of the angles obtained by dividing the angle by the diagonal is equal to:

(90 / (4 + 5)) * 4 = 40.

Let’s calculate what the larger of the angles is equal to:

90 – 40 = 50.

Let’s calculate how many degrees the angle between the diagonals, which is included in the triangle with the found angle of 40 °, is:

180 – (40 + 40) = 100.

Let’s calculate what the angle between the diagonals is equal to, which is included in the triangle with the found angle of 50 °:

180 – (50 + 50) = 80.

Answer: The smaller angle between the diagonals is 80 °, and the larger is 100 °.