△TUV

Question

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

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

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

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

m∠T=36°

Answer 1

In triangle △TUV, since it is isosceles with ∠T ≅ ∠V, we know that the measures of angles T and V are equal.

Given that m∠U = 54°, we can use the fact that the sum of the interior angles of a triangle is 180°:

\[ m∠T + m∠T + m∠U = 180° \] \[ 2m∠T + 54° = 180° \] \[ 2m∠T = 180° - 54° \] \[ 2m∠T = 126° \] \[ m∠T = \frac{126°}{2} \] \[ m∠T = 63° \]

So, the measure of angle T is 63°.

The correct answer is: m∠T = 63°.