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In the top triangle, the angle supplemental to 130°  = 50°

So.....the other angle in the top triangle is    = 85°

And in the quadrilatral, the angle supplemental to this =  95°

And in the leftmost triangle, again, the angle supplemental to 130° is 50°

So the missing angle in the triangle   is   180 - 50 - 30  = 100°

And the angle supplemental to this in the quadrilateral  = 80°

So.....the sum of the interior angles in the quadrilateral =  360

So we have that

360  = 95 + 80 + 130 + x      simplify

360  = 305 + x       subtract  305 from both sides

55°   = x