In triangle \( \triangle TUV \), we know that it is isosceles with \( \angle T \cong \angle V \) and that \( m\angle U = 54^\circ \).
Since the sum of the angles in any triangle is \( 180^\circ \), we can set up the following equation:
\[ m\angle T + m\angle V + m\angle U = 180^\circ \]
Because \( \angle T \) and \( \angle V \) are congruent, we can represent them as:
\[ m\angle T + m\angle T + 54^\circ = 180^\circ \]
This simplifies to:
\[ 2m\angle T + 54^\circ = 180^\circ \]
Subtracting \( 54^\circ \) from both sides gives us:
\[ 2m\angle T = 180^\circ - 54^\circ \] \[ 2m\angle T = 126^\circ \]
Dividing both sides by \( 2 \):
\[ m\angle T = 63^\circ \]
Thus, the measure of \( \angle T \) is:
\[ m\angle T = 63^\circ \]
The correct response is:
m∠T=63°