Question

What is the value of x?

A.5
B.10
C.13
D.15

Answer 1

The central angle is always double the arc. The answer is 13. C
Hope this helps!

Answer 2

(C) x=13

Explanation:

Given: A circle with inscribed angle that is ∠GFE=(6x-8)° and intercepted arc=(10x+10)°.

To find: The value of x.

Solution: We know that the measure of the inscribed angle is equal to the half of the measure of the intercepted arc, thus

m∠GFE=mGE

⇒
`(6x-8)^(\circ)=(1)/(2)(10x+10)^(\circ)`

⇒
`(6x-8)^(\circ)=(5x+15)^(\circ)`

⇒
`6x-8=5x+5`

⇒
`6x-5x=5+8`

⇒
`x=13`

Thus, the value of x is 13.