Question

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

Explanation:

Step1: Recall angle - sum property of a circle

The sum of the central angles of a circle is 360°. Since \(\overline{ST}\) is a diameter, the non - overlapping central angles \((2x + 8)^{\circ}+(3x - 14)^{\circ}+(3x - 14)^{\circ}=180^{\circ}\) (a straight - line angle formed by the diameter).

Step2: Combine like terms

Combine the \(x\) terms and the constant terms: \((2x+3x + 3x)+(8-14 - 14)=180\).
\(8x-20 = 180\).

Step3: Solve for \(x\)

Add 20 to both sides of the equation: \(8x-20 + 20=180 + 20\).
\(8x=200\).
Divide both sides by 8: \(x=\frac{200}{8}=25\).

Answer:

25.0