To find the measure of the obtuse angle \( b \) when given angles \( b \) and \( 250^\circ \), we first note that an obtuse angle is an angle that is more than \( 90^\circ \) but less than \( 180^\circ \).
However, the information you've provided is unclear as to what relationship exists between \( b \) and \( 250^\circ \). If the context is that two angles, \( b \) and \( 250^\circ \), are supplementary, meaning they add up to \( 180^\circ \), we can formulate it as follows:
\[ b + 250^\circ = 180^\circ \]
This equation simplifies to:
\[ b = 180^\circ - 250^\circ \] \[ b = -70^\circ \]
Since \( b \) cannot be a negative angle and must be measured within the standard \( 0^\circ \) to \( 360^\circ \) measure, it indicates that \( b \) could instead be an angle in the \( 360^\circ \) system. Since \( b \) must be obtuse but less than \( 360^\circ \), this isn't helpful.
Actually, if \( b \) is an angle which is paired with \( 250^\circ \), they might not directly supplement to \( 180^\circ \) but are rather coexisting angles on a circle.
Thus in a geometric context, \( b \) should be equal to \( 250^\circ - 180^\circ \) to find an angle less than \( 360^\circ\).
\[ b = 250^\circ - 180^\circ = 70^\circ \]
However, \( 70^\circ \) is not obtuse. Therefore, we must realize that \( b \) being obtuse means taking into consideration the \( 250^\circ \) angle placed on a circle rotation.
Since \( 250^\circ \) itself is an obtuse angle, but if \( b \) is to be obtuse in a different interpretation, measuring the other way around the circle gives us:
\[ b = 360^\circ - 250^\circ = 110^\circ \]
Thus, \( b \) would be \( 110^\circ \), which is indeed an obtuse angle.
So, the measure of the obtuse angle \( b \) is:
\[ b = 110^\circ. \]