△TUV is isosceles, with ∠T≅∠V and m∠U=54° . What is m∠T ?(1 point) Responses m∠T=54° m angle upper T equals 54 degrees m∠T=36° m angle upper T equals 36 degrees m∠T=126° m angle upper T equals 126 degrees m∠T=63°

1 answer

In triangle \( \triangle TUV \), it is given that \( \angle T \cong \angle V \) and \( m\angle U = 54^\circ \). Since \( \triangle TUV \) is isosceles with \( \angle T \) and \( \angle V \) as the equal angles, we can denote \( m\angle T = m\angle V = x \).

The sum of the angles in any triangle is \( 180^\circ \). Thus, we have:

\[ m\angle T + m\angle V + m\angle U = 180^\circ \]

Substituting in the known values:

\[ x + x + 54^\circ = 180^\circ \]

This simplifies to:

\[ 2x + 54^\circ = 180^\circ \]

Now, subtract \( 54^\circ \) from both sides:

\[ 2x = 126^\circ \]

Next, divide by 2:

\[ x = 63^\circ \]

So, \( m\angle T = 63^\circ \).

Therefore, the correct response is:

m∠T = 63°.