Question

Angles of Similar Triangles Quick Check
4 of 54 of 5 Items
Question
△TUV
is isosceles, with ∠T≅∠V
and m∠U=54°
. What is m∠T
?(1 point)
Responses

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

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

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

m∠T=126°

Answer 1

In triangle \( \triangle TUV \), since it is isosceles and \( \angle T \cong \angle V \), this means both angles \( T \) and \( V \) are equal.

Given that \( m\angle U = 54^\circ \), we can use the properties of triangles to find the measures of the other angles.

The sum of the angles in a triangle is always \( 180^\circ \). Hence, we can set up the equation as follows:

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

Since \( m\angle T = m\angle V \), we can let \( m\angle T = m\angle V = x \). Thus, we have:

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

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:

\[
x = 63^\circ
\]

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

The correct response is:

**m∠T=63°**