In an isosceles triangle, the angles opposite the equal sides are also equal. Given that triangle \( \Delta TUV \) is isosceles with \( \angle T \cong \angle V \) and \( m\angle U = 54^\circ \), we can find \( m\angle T \) as follows:
Let \( m\angle T = m\angle V = x \).
According to the triangle sum theorem, the sum of the angles in a triangle is \( 180^\circ \):
\[ m\angle T + m\angle V + m\angle U = 180^\circ \]
Substituting the known values:
\[ x + x + 54^\circ = 180^\circ \]
This simplifies to:
\[ 2x + 54^\circ = 180^\circ \]
Now, subtract \( 54^\circ \) from both sides:
\[ 2x = 180^\circ - 54^\circ \] \[ 2x = 126^\circ \]
Dividing both sides by 2 gives:
\[ x = 63^\circ \]
Thus, \( m\angle T = 63^\circ \).
The answer is:
m∠T = 63°.