what is the value of x? x =

Explanation:

Step1: Recall central - inscribed angle relationship

The measure of a central angle is twice the measure of an inscribed angle subtended by the same arc. Here, the inscribed angle $\angle HIG = 52^{\circ}$, and the central angle $\angle HFG=5x + 94^{\circ}$. So, $5x+94^{\circ}=2\times52^{\circ}$.

Step2: Simplify the equation

First, calculate $2\times52^{\circ}=104^{\circ}$. The equation becomes $5x+94 = 104$.

Step3: Solve for x

Subtract 94 from both sides of the equation: $5x=104 - 94$. So, $5x = 10$. Then divide both sides by 5: $x=\frac{10}{5}=2$.

Answer:

$2$