Question

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

Explanation:

Step1: Recall circle - angle property

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

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: \(8x-20 + 20=180 + 20\), so \(8x=200\).
Then divide both sides by 8: \(x=\frac{200}{8}=25\).

Answer:

25.0