Question

△TUV
is isosceles, with ∠T≅∠V and m∠U=54
∘
. What is m∠T?

A. m∠T=63
∘
B. m∠T=36
∘
C. m∠T=126
∘
D. m∠T=54
∘

Answer 1

In an isosceles triangle, the two angles opposite the equal sides are equal. Given that △TUV is isosceles with ∠T ≅ ∠V, we can denote the measures of these angles as m∠T = m∠V.

We know from the problem that m∠U = 54°. The sum of the angles in any triangle is always 180°. Therefore, we can set up the equation:

\[
m∠T + m∠T + m∠U = 180°
\]

Substituting the known value of m∠U:

\[
m∠T + m∠T + 54° = 180°
\]

This simplifies to:

\[
2m∠T + 54° = 180°
\]

Next, we subtract 54° from both sides:

\[
2m∠T = 180° - 54°
\]
\[
2m∠T = 126°
\]

Now, divide by 2 to find m∠T:

\[
m∠T = \frac{126°}{2} = 63°
\]

Therefore, the measure of angle T is:

\[
\boxed{63°}
\]

So the correct answer is **A. m∠T = 63°**.