Question

what is the value of x?

Explanation:

Step1: Recall the central - inscribed angle relationship

The measure of a central angle is twice the measure of the inscribed angle subtended by the same arc. Here, the central angle $\angle HJG = 11x - 45$ and the inscribed angle $\angle HIG=4x$. So, $11x - 45=2\times(4x)$.

Step2: Solve the equation

First, expand the right - hand side of the equation: $11x - 45 = 8x$. Then, subtract $8x$ from both sides: $11x-8x - 45=8x - 8x$, which simplifies to $3x-45 = 0$. Next, add 45 to both sides: $3x-45 + 45=0 + 45$, getting $3x=45$. Finally, divide both sides by 3: $x=\frac{45}{3}=15$.

Answer:

$15$