Question

Question was provided via image upload.

Explanation:

Step1: Identify triangle properties

$\triangle FGE$ is isosceles ($FG=EG$), so $\angle GFE = \angle GEF = x-15^\circ$. Also, $FE$ is a diameter, so $\angle FGE = 90^\circ$ (Thales' theorem).

Step2: Sum triangle angles

Sum of angles in a triangle is $180^\circ$.
$$(x-15^\circ) + (x-15^\circ) + 90^\circ = 180^\circ$$

Step3: Simplify and solve for x

Combine like terms and isolate $x$.
$$2x - 30^\circ + 90^\circ = 180^\circ$$
$$2x + 60^\circ = 180^\circ$$
$$2x = 120^\circ$$
$$x = 60^\circ$$

Answer:

$60$