The measure of the missing angle S is 65 degrees.
In isosceles trapezoid STUV, we know that:
Angle T is 115 degrees (given)
Opposite angles in a trapezoid are supplementary, meaning they add up to 180 degrees
Therefore, to find the measure of angle S, we can use the following steps:
Apply the angle addition property to angles T and S:
S + T = 180°
Substitute the known value of angle T:
S + 115° = 180°
Solve for angle S:
S = 180° - 115°
S = 65°
Therefore, the measure of the missing angle S is 65 degrees.