(1) The problem actually tells us that the 2 lines intersect at point E. The vertex of an angle is always the intersection of two different lines (or parts of lines) unless it is a straight (180 degrees) angle.
We know this is not a straight angle because we have a diagonal line intersecting a horizontal line.
(2) The name of the angle is given as 'angle AEC'. The middle letter of an angle name is always the vertex point of the angle.
