imc

We can let $\angle AEB$ be $4x$ and $\angle ABE$ be $5x$ because they are in the ratio $4:5$. When an inscribed angle contains the diameter, the inscribed angle is a right angle. Therefore by triangle sum theorem, $4x+5x+90=180⟶x=10$ and $\angle ABE=50$. $\angle ABE=\angle BED$ because they are alternate interior angles and $\overline{AB}\parallel \overline{ED}$. Opposite angles in a cyclic quadrilateral are supplementary, so $\angle BED+\angle BCD=180$. Use substitution to get $\angle ABE+\angle BCD=180⟶50+\angle BCD=180⟶\angle BCD=\boxed{130}$