Let's break down the problem step by step.

You have a triangle with three angles:

1. The top angle is $9x - 30^\circ$.
2. The bottom-left angle is $x + 5^\circ$.
3. The last angle is $4x - 38^\circ$, and it's supplementary to the bottom-left angle.

Step 1: Use the fact that the sum of interior angles of a triangle is always $180^\circ$.

This means:

$(9x - 30^\circ) + (x + 5^\circ) + (4x - 38^\circ) = 180^\circ$

Step 2: Simplify the equation:

$9x - 30 + x + 5 + 4x - 38 = 180$

[ 9x + x + 4x - 30 + 5 - 38 = 180 \