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

Question

Responses

A) m∠T=63°

B) m∠T=126°

C) m∠T=54°

D) m∠T=36°

Answer 1

Since ∠T≅∠V, we know that m∠T = m∠V.

Since ∆TUV is isosceles, the base angles ∠T and ∠V are congruent.

Using the isosceles triangle theorem, we know that the sum of the measures of the base angles in an isosceles triangle is 180°.

Therefore, m∠T + m∠V + m∠U = 180°.

Substituting the known values, we have:

m∠T + m∠T + 54° = 180°.

Combining like terms, we get:

2m∠T + 54° = 180°.

Subtracting 54° from both sides, we have:

2m∠T = 126°.

Dividing both sides by 2, we get:

m∠T = 63°.

Therefore, the answer is:

A) m∠T=63°.