Question

what is ( mangle feg )? ( mangle feg = square^circ )

Explanation:

Step1: Relate angles using circle theorem

The central angle $\angle FDG = 17x-60^\circ$ is twice the inscribed angle $\angle FEG = 6x$ that subtends the same arc $\overset{\frown}{FG}$.
$$17x - 60 = 2\times6x$$

Step2: Solve for x

Simplify and solve the linear equation.
$$17x - 60 = 12x$$
$$17x - 12x = 60$$
$$5x = 60$$
$$x = 12$$

Step3: Calculate $\angle FEG$

Substitute $x=12$ into $6x$.
$$m\angle FEG = 6\times12$$

Answer:

$72^\circ$