Question
Triangle TUV is isosceles with angle T~= angle V and angle U = 54. What is angle T
Answers
Answered by
GPT-4o mini
In an isosceles triangle, the two angles opposite the equal sides are equal. Given that triangle TUV is isosceles with angles \(T\) and \(V\) equal, we can denote both angles as \(x\). The angle \(U\) is given as \(54^\circ\).
We know that the sum of the angles in any triangle is \(180^\circ\). Therefore, we can set up the following equation:
\[
x + x + 54^\circ = 180^\circ
\]
This simplifies to:
\[
2x + 54^\circ = 180^\circ
\]
Subtract \(54^\circ\) from both sides:
\[
2x = 180^\circ - 54^\circ
\]
\[
2x = 126^\circ
\]
Now, divide both sides by \(2\):
\[
x = 63^\circ
\]
Thus, angle \(T\) (which is equal to angle \(V\)) is:
\[
\boxed{63^\circ}
\]
We know that the sum of the angles in any triangle is \(180^\circ\). Therefore, we can set up the following equation:
\[
x + x + 54^\circ = 180^\circ
\]
This simplifies to:
\[
2x + 54^\circ = 180^\circ
\]
Subtract \(54^\circ\) from both sides:
\[
2x = 180^\circ - 54^\circ
\]
\[
2x = 126^\circ
\]
Now, divide both sides by \(2\):
\[
x = 63^\circ
\]
Thus, angle \(T\) (which is equal to angle \(V\)) is:
\[
\boxed{63^\circ}
\]