Explanation:
when intersecting 2 parallel lines by a third line the angles at the intersection points must be the same at both lines. otherwise they are not parallel, or the third one is not a straight line.
the second thing to know : all angles in top of a line (or below a line) are in sum 180 degrees. this is what is needed to e.g. rotate a stick around a point on the line from one side to the other.
knowing all this we then know, that the angle right "under" the (8x -9) degree angle is also 53 degrees (or the angle above the 53 degree angle is (8x - 9) degrees).
and we know then that the sum of both angles is 180 degrees.
(8x - 9) + 53 = 180
8x - 9 = 127
8x = 136
x = 17