△TUV is isosceles, with ∠T≅∠V and m∠U=54°. What is m∠T?(1 point)
1.m∠T=126°
2.m∠T=36°
3.m∠T=63°
4.m∠T=54°
Since TUV is an isosceles triangle, ∠T and ∠V are congruent. Also, the sum of the angles in a triangle is 180°.
Let's denote ∠T = x and ∠V = x.
Since ∠U = 54°, the sum of the three angles is 54° + x + x = 180°.
Simplifying the equation, we get 54° + 2x = 180°.
Subtracting 54° from both sides, we get 2x = 126°.
Dividing both sides by 2, we get x = 63°.
Therefore, m∠T = m∠V = x = 63°.
So the answer is 3. m∠T = 63°.
Since ∆TUV is an isosceles triangle with ∠T ≅ ∠V, we know that m∠T = m∠V. We also know that m∠T + m∠U + m∠V = 180° (the sum of angles in a triangle is 180°).
Given that m∠U = 54°, we can substitute it into the equation above:
m∠T + 54° + m∠T = 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, the answer is 3. m∠T = 63°.