In triangle \( \triangle TUV \), since it is isosceles with \( \angle T \cong \angle V \), we know that the two base angles (angles T and V) are equal. Given that the measure of angle \( U \) is \( m\angle U = 54^\circ \), we can use the fact that the sum of the angles in any triangle is \( 180^\circ \).
Let \( m\angle T = m\angle V = x \). Then we have the equation:
\[ m\angle T + m\angle V + m\angle U = 180^\circ \]
Substituting the known values:
\[ x + x + 54^\circ = 180^\circ \]
This simplifies to:
\[ 2x + 54^\circ = 180^\circ \]
Subtract \( 54^\circ \) from both sides:
\[ 2x = 180^\circ - 54^\circ \] \[ 2x = 126^\circ \]
Dividing by 2:
\[ x = 63^\circ \]
Thus, \( m\angle T = 63^\circ \).
The correct response is:
m∠T = 63°.