In a rectangle, the angle between the diagonals and the larger side is 38 °.

In a rectangle, the angle between the diagonals and the larger side is 38 °. Find the smaller of the angles formed by the diagonals of the rectangle.

When the diagonals intersect in a rectangle, two pairs of isosceles triangles and two pairs of equal angles are formed. By condition, we know that the angle at the base of one of these isosceles triangles is 38 °, which means that the angle at the apex will be equal to:
180 ° – (38 ° + 38 °) = 180 ° – 76 ° = 104 °.
This will be one of the corners formed by the diagonals of the rectangle.
The angles are adjacent to each other, find the second angle:
180 ° – 104 ° = 76 °.
Answer: The smaller of the angles formed by the diagonals is 76 °.