To find the measure of angle TSV, we can use the fact that the sum of the angles around a point is 360 degrees.
∠TSV + ∠RSV + ∠RST = 360 degrees
We are given that:
∠TSR = 157 degrees
∠VSR = 54 degrees
Substitute these values into the equation:
∠TSV + 54 degrees + 157 degrees = 360 degrees
∠TSV + 211 degrees = 360 degrees
Subtract 211 degrees from both sides:
∠TSV = 149 degrees
Therefore, the measure of ∠TSV is 149 degrees.