Explanation:
when a line cuts through 2 parallel lines, it does the exact same thing to both lines. it has to. because they are parallel, they act as if they are identical. only their placement is different, but this has no impact on the angles between the lines.
now, imagine a circle with the center at one of the crossing points. this circle is cut in half by the central line.
you know how many degrees a full circle has ?
360 degrees.
now, how many degrees are represented by the half- circle above or below the center line ?
of course, half of the degrees of the full circle. that means 180 degrees.
so, all the angles around a single point on one side of a line must have how many degrees together ?
right, these half-circle 180 degrees again.
because of everything we said up there, the angle 4x+6 is the same as the angle right of the 7x-2 angle.
so, 7x-2 and 4x+6 must be 180 degrees together.
that is called "supplementary angles".
7x - 2 + 4x + 6 = 180
11x = 176
x = 16