To find the obtuse angle \( v \) given that \( v \) and \( 245^\circ \) are supplementary angles, we can use the property that supplementary angles add up to \( 180^\circ \).
The equation can be set up as follows:
\[ v + 245^\circ = 180^\circ \]
To find \( v \), subtract \( 245^\circ \) from \( 180^\circ \):
\[ v = 180^\circ - 245^\circ \]
Calculating this gives:
\[ v = 180^\circ - 245^\circ = -65^\circ \]
However, \( v \) being negative doesn't make sense in the context of angles. Instead, we realize that since \( v \) is supposed to be the obtuse angle (greater than 90°), we should consider the related acute angle to \( 245^\circ \).
Since \( 245^\circ \) is actually an obtuse angle, the corresponding angle in the range of \( 0^\circ \) to \( 360^\circ \) can be defined as:
\[ v = 245^\circ - 180^\circ = 65^\circ \quad \text{(this is acute)} \]
To find the obtuse angle in the second quadrant that is supplementary to \( 245^\circ \):
\[ v = 360^\circ - 245^\circ = 115^\circ \]
Thus, the measure of the obtuse angle \( v \) is:
\[ v = 115^\circ \]