In the cube ABCD-A1B1C1D1, why is the angle between AD1 and DC1 60 degrees? Can you explain in detail?

Connect AB1, B1D1

Because AD is parallel and equal to B1C1

The quadrilateral ADC1B1 is a parallelogram.

So DC1 is parallel and equal to AB1

So the angle between AD1 and DC1 is converted into ∠D1AB1

Because AD1, AB1, B1D1 are all square diagonal. And all six faces of the cube are equal.

So AD1=AB1=B1D1

So the triangle AB1D1 is an equilateral triangle

So ∠D1AB1=60°

That is, the relationship between AD1 and DC1 The angle is 60°