Question

what is the value of x?

Explanation:

Step1: Identify the triangle type

Since \( UT = UV \), \(\triangle TUV\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle T=\angle V = 65^{\circ}\). Using the formula \(\angle T+\angle V+\angle U=180^{\circ}\), but since we need \(x = \angle V\) (as per the problem's notation where \(x\) is at vertex \(V\)) and from the property of isosceles triangle \(x=\angle T\).

Answer:

\(65\)