△TUV is isosceles, with ∠T≅∠V and m∠U=54°. What is m∠T?
Since ∠T ≅ ∠V in an isosceles triangle, we know that m∠T = m∠V. Also, since ∠TUV is a triangle, the sum of all interior angles is 180°.
Let's use this information to solve for ∠T:
m∠T + m∠V + m∠U = 180°
Since ∠T ≅ ∠V:
m∠T + m∠T + m∠U = 180°
Substituting the given value for m∠U:
m∠T + m∠T + 54° = 180°
Simplifying the equation:
2m∠T + 54° = 180°
Subtracting 54° from both sides:
2m∠T = 126°
Dividing both sides by 2:
m∠T = 63°
Therefore, m∠T is 63°.