△TUV


T
U
V
is isosceles, with ∠T≅∠V

T


V
and m∠U=54°
m

U
=
54
°
. What is m∠T
m

T
?(1 point)
Responses

m∠T=54°
m

T
=
54
°
m angle upper T equals 54 degrees

m∠T=63°
m

T
=
63
°
m angle upper T equals 63 degrees

m∠T=126°
m

T
=
126
°
m angle upper T equals 126 degrees

m∠T=36°

1 answer

In triangle \( \triangle TUV \), we know that it is isosceles with \( \angle T \cong \angle V \) and that \( m\angle U = 54^\circ \).

Since the sum of the angles in any triangle is \( 180^\circ \), we can set up the following equation:

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

Because \( \angle T \) and \( \angle V \) are congruent, we can represent them as:

\[ m\angle T + m\angle T + 54^\circ = 180^\circ \]

This simplifies to:

\[ 2m\angle T + 54^\circ = 180^\circ \]

Subtracting \( 54^\circ \) from both sides gives us:

\[ 2m\angle T = 180^\circ - 54^\circ \] \[ 2m\angle T = 126^\circ \]

Dividing both sides by \( 2 \):

\[ m\angle T = 63^\circ \]

Thus, the measure of \( \angle T \) is:

\[ m\angle T = 63^\circ \]

The correct response is:

m∠T=63°