In triangle \( \triangle TUV \), since it is isosceles with \( \angle T \cong \angle V \), we can denote the measure of \( \angle T \) and \( \angle V \) as \( x \). Given that \( m\angle U = 54^\circ \), we can use the property that the sum of the angles in a triangle is \( 180^\circ \).
So, we have the equation: \[ x + x + 54^\circ = 180^\circ \] This simplifies to: \[ 2x + 54^\circ = 180^\circ \] Subtract \( 54^\circ \) from both sides: \[ 2x = 180^\circ - 54^\circ \] \[ 2x = 126^\circ \] Dividing both sides by 2 gives: \[ x = 63^\circ \]
Thus, \( m\angle T = 63^\circ \).
The correct answer is:
m∠T = 63°