△TUV

is isosceles, with ∠T≅∠V
and m∠U=54°
. What is m∠T
?(1 point)
Responses

m∠T=126°
m angle upper T equals 126 degrees

m∠T=36°
m angle upper T equals 36 degrees

m∠T=54°
m angle upper T equals 54 degrees

m∠T=63°

1 answer

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

Since the sum of the angles in any triangle is always \( 180^\circ \), we can express this as:

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

Let \( m\angle T = m\angle V = x \). Then we can replace \( m\angle U \) with \( 54^\circ \):

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

This simplifies to:

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

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

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

Now, divide by 2:

\[ x = 63^\circ \]

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

Therefore, the correct response is:

m∠T = 63°.