In rectangle ABCD diagonals AC and BD intersect at point O. angle AOB = 40, find angle DAO =?

Let’s consider different options for solving the problem.
Option 1.
Knowing that the diagonals in the rectangle form two pairs of isosceles triangles, consider one of them, the triangle AOB. In it, by condition, we know the angle at the top, we can find the angle at the base:
ВАО angle = (180 ° – 40 °) / 2 = 70 °.
Find the angle DAO:
DAO angle = 90 ° – 70 ° = 20 °.

Option 2.
Find the angle AOD (adjacent to the angle AOB):
Angle AOD = 180 ° – angle AOB = 180 ° – 40 ° = 140 °.
Consider an isosceles triangle AOD, in which we know the angle at the apex, we can find the angle at the base:
DAO angle = (180 ° – 140 °) / 2 = 20 °.
Answer: DAO angle 20 °.