△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=63°
m angle upper T equals 63 degrees

m∠T=126°

1 answer

In triangle \( \triangle TUV \), since it is isosceles with \( \angle T \cong \angle V \), we know that the two base angles (angles T and V) are equal. Given that the measure of angle \( U \) is \( m\angle U = 54^\circ \), we can use the fact that the sum of the angles in any triangle is \( 180^\circ \).

Let \( m\angle T = m\angle V = x \). Then we have the equation:

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

Substituting the known values:

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

This simplifies to:

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

Subtract \( 54^\circ \) from both sides:

\[ 2x = 180^\circ - 54^\circ \] \[ 2x = 126^\circ \]

Dividing by 2:

\[ x = 63^\circ \]

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

The correct response is:

m∠T = 63°.