1. The problem involves understanding the relationship between angle $b$ and the right angle in a triangle or geometric figure. 2. A vertical angle is formed when two lines intersect, and vertical angles are always equal. 3. Since $b$ is a vertical angle next to the right angle, it means $b$ is equal to the right angle. 4. The right angle measures $90^\circ$, so by the property of vertical angles, $b = 90^\circ$. 5. Therefore, angle $b$ is $90$ degrees because vertical angles are congruent.