In an isosceles triangle, two sides are equal, and the angles opposite those sides are also equal. Given triangle TUV is isosceles with \( T \sim V \), this means that angles T and V are equal.
Let's denote the measure of angle T and angle V as \( x \). Since the sum of the angles in a triangle is 180 degrees, we can set up the following equation:
\[ x + x + 54 = 180 \]
This simplifies to:
\[ 2x + 54 = 180 \]
Subtracting 54 from both sides gives:
\[ 2x = 126 \]
Dividing by 2, we find:
\[ x = 63 \]
Therefore, the measurement of angle T is 63 degrees.
So, the correct answer is 63.