Why did radical Republicans believe that Andrew Johnson would support their agenda?
I assume that you are asking about the radicals' agenda with regard to Reconstruction and the South. If so, the radical Republicans thought that President Johnson would support their agenda because he was known to hate the Southern elites.
President Johnson was himself a Southerner. However, he was not a member of the elites. Instead, he came from a poor family and had no education. He made his living at first as a tailor. Because of this, he had no love for the Southern planter elite. The radical Republicans believed that this animosity towards the elites of the South would translate to support for their desire to treat the South harshly during Reconstruction. They were, of course, wrong, and Johnson would defy them, leading to his impeachment.