Question

Calculate the value of x in the illustration below.

Answer 1

`x=8.75`

Explanation:

We have been given a circle. We are asked to find the value of x for our given circle.

Upon looking at our given circle, we can see that angle RCS is an inscribed angle of arc RS.

We know that measure of an inscribed angle is half the measure of its intercepted arc, so we can set an equation as:

`m\angle RCS=\frac{\widehat{RS}}{2}`

`6x^(\circ)=(105^(\circ))/(2)`

`6x^(\circ)=52.5^(\circ)`

`(6x^(\circ))/(6)=(52.5^(\circ))/(6)`

`x^(\circ)=8.75^(\circ)`

`x=8.75`

Therefore, the value of x is 8.75 for the given circle and option A is the correct choice.

Answer 2

x = 8.75

Explanation:

The measure of angle C is half the measure of arc RS, so ...

6x = (1/2)(105)

x = 105/12 = 8.75 . . . . divide by 6