Question

Point C is the center of the circle. Arc AB measures 5x + 2. Angle ACB measures 3x + 14. Find the value of x

Answer 1

I think you can find it out with this formula :

5x + 2 = 3x + 14

5x - 3x  = 14 - 2

2 x     = 12

x = 6

Hope this helps

Answer 2

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.