Let's analyze the given problem and solve it step by step. The key provided information is:

• $m \angle DBE = 50^\circ$
• The diagram shows relationships involving $x$ and $y$.

We will proceed in order:

16. $m \angle BED$:

• Angle $BED$ and $DBE$ are vertical angles because they intersect at $B$.
• Vertical angles are congruent.

Thus:
$m \angle BED = m \angle DBE = 50^\circ.$

17. $m \angle BEA$:

• $BEA$ is a straight angle composed of angles $BED$ and $DEA$.
  Since $BEA$ is a straight line, its measure is $180^\circ$.

We know:
$m \angle BEA = m \angle BED + m \angle DEA.$ Here $\angle BED = 50^\circ$, and by symmetry or splitting into congruent parts, $\angle DEA = 50^\circ$.

Thus:
$m \angle BEA = 50^\circ + 50^\circ = 100^\circ.$

18. Solve for $x$:

From the triangle $ABE$, we see that segments marked with equal lines suggest congruency properties.

The diagram includes expressions like $6x - 2$. We need to set up the congruent side conditions to solve $x$. Given the symmetry and congruence relationships, let me confirm:

[ x = ... (WILL **