the angle ABC = 180 - x, as ABD and ABC are complementary angles on top of the bottom line : all angles around a point on one side of a line are always adding up to 180 degrees.
but because we also know that the sum of all angles in a triangle is 180 degrees too, we can say
A translation is sliding around or moving around/shifting so the first one is translation. A rotation is spinning it around to a different angle so the second is a rotation. Hope this helps!!