smc

We first consider $\angle CBA$. Because $\angle A=55$ and $\angle C=75$, $\angle B=180-55-75=50$. Then, because $△BED$ is isosceles, we have the equation $2\angle BED+50=180$. Solving this equation gives us $\angle BED=65\to \boxed{65^{\circ }}$