ABCD is a rectangle with AC =10 cm and BC=8cm. Diagonals AC and BD intersect at E and D2=20°. Calculate the sizes of all interior angles and AD,AE and AB? D1=70° how can I find A1 and A2,B1 and B2 ?

To find the sizes of all interior angles and the lengths of AD, AE, and AB, we can use the properties of rectangles and the properties of triangles formed by the diagonals.

1. Interior angles:
- Angle A1 = Angle A2 = 90 degrees (since ABCD is a rectangle)
- Angle B1 = Angle B2 = 90 degrees (since ABCD is a rectangle)
- Angle D1 = 70 degrees (given)
- Angle D2 = 20 degrees (given)

2. Lengths of AD, AE, and AB:
- Since ABCD is a rectangle, AD = BC = 8 cm
- AE = AC = 10 cm
- AB = BD = √(AD^2 + BD^2) = √(8^2 + 10^2) = √(64 + 100) = √164 ≈ 12.81 cm

To find the values of A1, A2, B1, and B2, we can use the properties of triangles formed by the diagonals. In triangle ADE:
- Angle A1 + Angle D1 + Angle D2 = 180 degrees (sum of angles in a triangle)
- Angle A1 + 70 + 20 = 180
- Angle A1 = 90 degrees

Similarly, in triangle ABE:
- Angle A2 + Angle B1 + Angle B2 = 180 degrees (sum of angles in a triangle)
- Angle A2 + 90 + 90 = 180
- Angle A2 = 0 degrees

Therefore, the values of A1, A2, B1, and B2 are:
- A1 = 90 degrees
- A2 = 0 degrees
- B1 = 90 degrees
- B2 = 0 degrees