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

Responses

m∠T=63°
  m angle upper T equals 63 degrees

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

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

m∠T=126°

1 answer

In an isosceles triangle, the angles opposite the equal sides are also equal. Given that triangle \( \Delta TUV \) is isosceles with \( \angle T \cong \angle V \) and \( m\angle U = 54^\circ \), we can find \( m\angle T \) as follows:

Let \( m\angle T = m\angle V = x \).

According to the triangle sum theorem, the sum of the angles in a triangle is \( 180^\circ \):

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

Substituting the known values:

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

This simplifies to:

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

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

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

Dividing both sides by 2 gives:

\[ x = 63^\circ \]

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

The answer is:

m∠T = 63°.