Question

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

Explanation:

Step1: Identify right triangle property

Since $TU$ is the diameter of the circle, $\angle TSU = 90^\circ$ (angle inscribed in a semicircle is a right angle).

Step2: Sum angles in triangle

The sum of angles in $\triangle TSU$ is $180^\circ$. Set up the equation:
$$35^\circ + 11x + 90^\circ = 180^\circ$$

Step3: Simplify and solve for x

Combine constant terms:
$$125^\circ + 11x = 180^\circ$$
Isolate the term with $x$:
$$11x = 180^\circ - 125^\circ = 55^\circ$$
Solve for $x$:
$$x = \frac{55^\circ}{11} = 5^\circ$$

Answer:

$x = 5$