Finding Angle B in Triangle ABC

In triangle ABC, angle A measures $45^\circ$, angle B measures $x$, and angle C measures $y$. The angles have the relationship where $y = 2x - 10^\circ$. Determine the value of angle B if the sum of the angles in triangle ABC equals $180^\circ$.

Using the triangle angle sum property, which states that the sum of the internal angles in any triangle is $180^\circ$, set up the equation:

$45^\circ + x + y = 180^\circ$