in which layer of the atmosphere do the radio wave signals bounces off? Explain the importance of this characteristic to use​

The ionosphere is ionized by solar radiation. It plays an important role in atmospheric electricity and forms the inner edge of the magnetosphere. It has practical importance because, among other functions, it influences radio propagation to distant places on the Earth.Hope it helps...

The peak above is part of the  sierra madre occidentals ,  a chain of volcanic mountains that runs through the middle of central america.