To find the measure of angle TSv, we can use the fact that adjacent angles (angles that share a common side and vertex) are supplementary. This means that the sum of the measures of adjacent angles equals 180 degrees.
Given:
- Angle TSR = 157 degrees
- Angle VSR = 54 degrees
To find angle TSv, we first note that angles TSv and VSR are adjacent angles. The sum of angles TSv and VSR is 180 degrees:
\[ \text{Angle TSv} + \text{Angle VSR} = 180^\circ \]
Substituting the measure of angle VSR:
\[ \text{Angle TSv} + 54^\circ = 180^\circ \]
Now, we can solve for angle TSv:
\[ \text{Angle TSv} = 180^\circ - 54^\circ \] \[ \text{Angle TSv} = 126^\circ \]
Thus, the measure of angle TSv is \(126\) degrees.