Answer:
[tex]x=6[/tex]
Step-by-step explanation:
Please find the attachment.
We have been given that point C is the center of the circle. Arc AB measures [tex]5x+2[/tex]. Angle ACB measures [tex]3x+14[/tex]. 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:
[tex]m\widehat{AB}=m\angle ACB[/tex]
[tex]5x+2=3x+14[/tex]
[tex]5x-3x+2=3x-3x+14[/tex]
[tex]2x+2=14[/tex]
[tex]2x+2-2=14-2[/tex]
[tex]2x=12[/tex]
[tex]\frac{2x}{2}=\frac{12}{2}[/tex]
[tex]x=6[/tex]
Therefore, the value of x is 6.
