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Supplementary angles add to 180deg

Interior angles of a triangle add to 180deg

Interior angles of a quadrilateral add to 360deg

The angle supplementary to 130° = 50°

So...the missing angle in the top triangle = 180 - 45 - 50 = 85°

And the angle supplemental to this is 95°

So....x = 180 - 95 - 30  =  180 - 125  =  55°

First...realize that 180-150=30 degrees, since it is a straight line. Since the angles in a triangle add up to 180, the angle in the topmost triangle is 180-30-45=105. Again, there is a straight line, so 180-105=95 degrees(one of the angles in the quadrilateral.)

Next, by opposite angle, the triangle to the leftmost has angles 30 degrees and 50 degrees, so the remaining measure is 180-30-50=100 degrees. And, 180-100=80 degrees.

Now, that we filled up the angles in the quadrilateral and trying to solve for x, we get 360-130-95-80=55 degrees.