Do not redefine x. The value of x is defined by the picture: x - 3 is the leftmost angle. There is no reason to believe that x is also the top angle.

I am afraid, this is an ill-posed problem because the only restriction is (x - 3) + 41 + (y + 8) = 180 (one equation with two unknowns). Here y + 8 can vary between 0 and 180 - 74 = 106 degrees (exclusive). Each value of y defines x uniquely, but without additional information, such as that the triangle is isosceles, I don't see why y has to be unique. In other words, the vertex of the 41 degrees' angle can slide left or right.

What do the arrows represent? Is this the path of light reflecting from the horizontal line by chance? Then x - 3 = y + 8, but this does not fit any answer either...

Here you are redefining x again. The picture defines x as 1/22th of angle 8 (which, by assumption, is the same as 1/8th of angle 3). It is incorrect to say that xequalsangle 8. Instead, angle 3 + angle 8 = 8x + 22x = 30x = 180 degrees.

Continue the bottom inclined line to the intersection with line l. Then 56 is an exterior angle to the resulting triangle and, as such, equals the sum of the two interior angles adjacent to l.