In triangle \( \triangle TUV \), with \( \angle T \cong \angle V \) and \( m\angle U = 54^\circ \), we can use the fact that the sum of the interior angles of a triangle is always \( 180^\circ \).
Since \( \angle T \) and \( \angle V \) are congruent, we can let \( m\angle T = m\angle V = x \).
The sum of the angles in the triangle can be expressed as:
\[ m\angle T + m\angle U + m\angle V = 180^\circ \]
Substituting in the known values:
\[ x + 54^\circ + x = 180^\circ \]
This simplifies to:
\[ 2x + 54^\circ = 180^\circ \]
Now, subtract \( 54^\circ \) from both sides:
\[ 2x = 180^\circ - 54^\circ \] \[ 2x = 126^\circ \]
Next, divide by 2 to find \( x \):
\[ x = \frac{126^\circ}{2} = 63^\circ \]
Thus, \( m\angle T = 63^\circ \).
So, the measure of angle \( T \) is \( \boxed{63^\circ} \).
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