Question

what is the value of x?

Explanation:

Step1: Use inscribed - angle theorem

In a circle, angles in the same segment are equal. So, the angle $\angle UTS$ and $\angle UVS$ subtend the same arc $US$. We can set up an equation based on the equality of these angles.
$2x + 38^{\circ}=46^{\circ}$

Step2: Solve the equation for x

Subtract $38^{\circ}$ from both sides of the equation:
$2x=46^{\circ}- 38^{\circ}$
$2x = 8^{\circ}$
Divide both sides by 2:
$x=\frac{8^{\circ}}{2}=4^{\circ}$

Answer:

$4$