Answer:
(C) x=13
Step-by-step 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
⇒[tex](6x-8)^{\circ}=\frac{1}{2}(10x+10)^{\circ}[/tex]
⇒[tex](6x-8)^{\circ}=(5x+15)^{\circ}[/tex]
⇒[tex]6x-8=5x+5[/tex]
⇒[tex]6x-5x=5+8[/tex]
⇒[tex]x=13[/tex]
Thus, the value of x is 13.
