Answer:
\(x=6\)
Step-by-step explanation:
Please find the attachment.
We have been given that point C is the center of the circle. Arc AB measures \(5x+2\). Angle ACB measures \(3x+14\). We are asked to find the value of x.
Since point C is the center of circle, so angle ACB will be a central angle. We know that the measure of a central angle is equal to the measure of subtended arc.
We can set an equation as:
\(m\widehat{AB}=m\angle ACB\)
\(5x+2=3x+14\)
\(5x-3x+2=3x-3x+14\)
\(2x+2=14\)
\(2x+2-2=14-2\)
\(2x=12\)
\(\frac{2x}{2}=\frac{12}{2}\)
\(x=6\)
Therefore, the value of x is 6.
