if i know one angle between the diagonals at intersecting point , how can i find the angle between the sides and the diagonal?

If it is a rectangle then you have 4 isoceles triangles

T + 2 A = 180
where T is your given angles and A is your two angles at the sides. In the other two triangles the angle you want is 90-A

To find the angle between the sides of a quadrilateral and one of its diagonals, when you already know one angle between the diagonals at the intersecting point, you can follow these steps:

1. Start by drawing a quadrilateral with its diagonals intersecting at a point.
2. Identify the given angle between the diagonals at the intersecting point. Let's call this angle "x".

Now, to find the angle between one of the sides and the diagonal, you can use the following formula:

Angle between side and diagonal = (180 - x) / 2

Let's understand this formula:

In a quadrilateral, the sum of the angles at any given point is always 360 degrees. In our case, the intersecting point between the diagonals is formed by two angles, x and the angle between one of the sides and the diagonal. Therefore, the sum of these two angles should be equal to 180 degrees.

Since we know the given angle x, we can subtract it from 180 to get the remaining angle. Dividing this angle by 2 gives us the angle between one of the sides and the diagonal.

By using this formula, you can find the angle between one of the sides and the diagonal when you know the angle between the diagonals at the intersecting point.