Question

△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°

Answer 1

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°