In an isosceles triangle, the two base angles are equal. Given that \( \angle T \cong \angle V \) and \( m\angle U = 54^\circ \), we can find the measures of angles T and V.
The sum of the angles in a triangle is always \( 180^\circ \). So, we can write the equation:
\[ m\angle T + m\angle V + m\angle U = 180^\circ \]
Since \( m\angle T = m\angle V \), we can denote \( m\angle T = m\angle V = x \). Therefore, the equation becomes:
\[ x + x + 54^\circ = 180^\circ \]
This simplifies to:
\[ 2x + 54^\circ = 180^\circ \]
Subtract \( 54^\circ \) from both sides:
\[ 2x = 180^\circ - 54^\circ \]
\[ 2x = 126^\circ \]
Divide both sides by 2:
\[ x = 63^\circ \]
Thus,
\[ m\angle T = 63^\circ \]
The correct answer is \( m\angle T = 63^\circ \).
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