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