Question

in circle o, \\(\overline{st}\\) is a diameter. what must be the value of x? \\((2x + 8)\degree\\) \\((3x - 14)\degree\\) \\((3x - 14)\degree\\) \\(\bigcirc\\) 22.0 \\(\bigcirc\\) 25.0 \\(\bigcirc\\) 25.4 \\(\bigcirc\\) 37.2

Explanation:

Step1: Sum angles to 180°

Since $\overline{ST}$ is a diameter, the total measure of angles $\angle ROS$, $\angle ROU$, and $\angle UOT$ along the semicircle is $180^\circ$.
$$(2x + 8) + (3x - 14) + (3x - 14) = 180$$

Step2: Simplify the equation

Combine like terms on the left side.
$$2x + 3x + 3x + 8 - 14 - 14 = 180$$
$$8x - 20 = 180$$

Step3: Solve for x

Isolate the variable term, then solve for x.
$$8x = 180 + 20$$
$$8x = 200$$
$$x = \frac{200}{8}$$

Answer:

25.0