∆TUV is isosceles, with <T°=<V and m<U=54°. What is m<T?
Since ∆TUV is isosceles, this means that the base angles ∠T and ∠V are equal.
Let's assume ∠T = ∠V = x (since they are equal)
Therefore, the sum of the angles of a triangle is 180°. We can write the equation as follows:
∠T + ∠V + ∠U = 180°
x + x + 54° = 180°
2x + 54° = 180°
Subtracting 54° from both sides:
2x = 180° - 54°
2x = 126°
Dividing both sides by 2:
x = 126° / 2
x = 63°
Therefore, m<T = 63°.
To solve this problem, we will use the properties of isosceles triangles and the fact that the sum of the angles in a triangle is 180 degrees.
Given:
∆TUV is isosceles, so TV = TU.
We are also given that <T = <V.
And m<U = 54°.
To find m<T, we need to set up an equation and solve for m<T.
In ∆TUV, there are three angles: <T, <U, and <V.
Since ∆TUV is a triangle, the sum of the angles is 180 degrees.
So we can write the equation:
<T + <U + <V = 180°
Since <T = <V (given), we can substitute <V for <T in the equation:
<V + <U + <V = 180°
Simplifying the equation gives:
2<V + <U = 180°
We are also given that m<U = 54°.
Substituting this value in the equation:
2<V + 54° = 180°
Subtracting 54 from both sides:
2<V = 180° - 54°
2<V = 126°
Dividing both sides by 2:
<V = 63°
Since <T = <V (given), m<T = 63°.
Therefore, m<T = 63°.