Question

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

Explanation:

Step1: Recall angle - sum property of a circle

The sum of the central angles in 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 subtends an angle of 180° at the center of a circle).

Step2: Combine like terms

Combine the x - terms and the constant terms: $(2x+3x + 3x)+(8-14 - 14)=180$. Simplify to get $8x-20 = 180$.

Step3: Solve for x

Add 20 to both sides of the equation: $8x-20 + 20=180 + 20$, which gives $8x=200$. Then divide both sides by 8: $x=\frac{200}{8}=25$.

Answer:

25.0