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

`x=6`

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`

`(2x)/(2)=(12)/(2)`

`x=6`

Therefore, the value of x is 6.

Answer 2

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