what is the value of x?\n$x = \\square$

Answer:

$3$

Explanation:

Step1: Identify right angle

Since $ST$ is the diameter, $\angle SRT = 90^\circ$ (angle inscribed in a semicircle is a right angle).

Step2: Sum triangle angles

The sum of angles in $\triangle SRT$ is $180^\circ$. $$60^\circ + 90^\circ + 10x = 180^\circ$$

Step3: Solve for $x$

Simplify and isolate $x$: $$150^\circ + 10x = 180^\circ$$ $$10x = 180^\circ - 150^\circ$$ $$10x = 30^\circ$$ $$x = \frac{30^\circ}{10} = 3$$