Question

what is the value of x? x = \square^\circ

Explanation:

Step1: Identify right triangle property

Since side $VU$ passes through the circle's center, $\angle VTU = 90^\circ$ (angle inscribed in a semicircle is a right angle). Also, $VT = TU$, so $\triangle VTU$ is an isosceles right triangle, meaning $\angle TVU = \angle TUV$.

Step2: Set up angle sum equation

The sum of angles in a triangle is $180^\circ$.
$$90^\circ + (x+34^\circ) + (x+34^\circ) = 180^\circ$$

Step3: Simplify and solve for x

Combine like terms and isolate $x$.
$$90 + 2x + 68 = 180$$
$$2x + 158 = 180$$
$$2x = 180 - 158$$
$$2x = 22$$
$$x = \frac{22}{2} = 11$$

Answer:

$11$