I need to show that a set B is regular open if and only if its complement is regular closed.

=> Assume B is regular open => B = Int (cl B)

<= Assume C(B) is regular closed => B = cl (Int (B))

I know that C(Int B)= cl (C(B)) and Int (B)= C(cl C(B)) [The int B = the complement of the closure of the complement of B]

I'm just not sure how to relate those to what I have above.