Given:
The measure of angle EFG is [tex]m\angle EFG=(8x+1)^{\circ}[/tex]
The measure of arc GE is [tex]m\widehat{(GE})=(15+10)^{\circ}[/tex]
We need to determine the value of x.
Value of x:
The value of x can be determined using the inscribed angle theorem.
Thus, we have;
[tex]\angle EFG=\frac{1}{2}(\widehat{GE})[/tex]
Substituting the values, we have,
[tex]8x+1=\frac{1}{2}(15x+10)[/tex]
[tex]2(8x+1)=1(15x+10)[/tex]
[tex]16x+2=15x+10[/tex]
[tex]x+2=10[/tex]
[tex]x=8[/tex]
Hence, the value of x is 8.
Therefore, Option B is the correct answer.
