To find the measure of the obtuse angle \( v \), we first need to determine the relationship between the angles mentioned.
Given that \( x \) is an angle, and we know that the total measure of angles around a point is \( 360 \) degrees, we can express this as:
\[ x + v = 360^\circ \]
If \( v \) is to be the obtuse angle, it must be greater than \( 90^\circ \) but less than \( 180^\circ \).
Also, from your mention of \( 245 \) degrees, we recognize that it could be related as follows:
- If a straight line forms \( 180 \) degrees, the supplementary angle is calculated as \( 360 - 245 \) degrees.
Calculating that gives:
\[ 360^\circ - 245^\circ = 115^\circ \]
Since \( 115^\circ \) is indeed an obtuse angle (between \( 90^\circ \) and \( 180^\circ \)), it is a valid candidate for \( v \).
To summarize, we can conclude:
The measure of the obtuse angle \( v \) is:
\[ v = 115^\circ \]
Thus, the value of \( x \) must be:
\[ x = 360^\circ - v = 360^\circ - 115^\circ = 245^\circ \]
So, the measures are:
- \( v = 115^\circ \)
- \( x = 245^\circ \)
In conclusion, the measure of the obtuse angle \( v \) is \( \boxed{115} \) degrees.