To solve for angle $HJG$, we analyze the given information in the problem:

Given:

1. $EFG$ is a triangle.
2. $HJ$ is parallel to $FG$.
3. Angle $FEG = 75^\circ$.
4. Angle $EFG = 2x^\circ$.
5. Angle $FGE = (x + 15)^\circ$.

Step 1: Solve for $x$

In any triangle, the sum of interior angles is $180^\circ$. For triangle $EFG$: $\text{Angle } FEG + \text{Angle } EFG + \text{Angle } FGE = 180^\circ$ Substitute the values: $75^\circ + 2x^\circ + (x + 15)^\circ = 180^\circ$ Simplify: $75 + 2x + x + 15 = 180$ $3x + 90 = 180$ $3x = 90$ $x = 30$

Step 2: Find specific angles in triangle $EFG$

Now substitute (x = 30