We are given a figure where line segment $AB$ is parallel to line segment $CD$. We are also given that $\angle ABE = 50^{\circ}$ and $\angle CDE = 35^{\circ}$. We need to find the measure of $\angle BED$.

1. Problem Description

We are given a figure where line segment $AB$ is parallel to line segment $CD$. We are also given that $\angle ABE = 50^{\circ}$ and $\angle CDE = 35^{\circ}$. We need to find the measure of $\angle BED$.

2. Solution Steps

Since $AB$ is parallel to $CD$, we know that alternate interior angles are congruent.

However, it is not immediately obvious how this applies to the solution.

Instead, draw a line through $E$ that is parallel to $AB$ and $CD$. Let's call this line $FEG$ where $F$ is on the same side as $A$ and $G$ is on the same side as $C$.

Since $AB \parallel FEG$, $\angle ABE = \angle BEF = 50^{\circ}$ (alternate interior angles).

Since $CD \parallel FEG$, $\angle CDE = \angle DEG = 35^{\circ}$ (alternate interior angles).

We know that $\angle BED = \angle BEF + \angle DEG$.

Therefore, $\angle BED = 50^{\circ} + 35^{\circ} = 85^{\circ}$.

3. Final Answer

The measure of $\angle BED$ is $85^{\circ}$.

The answer is B.