Final answer:
Without additional context, such as the location of point X, options a and b cannot be accurately validated, and option c is not true since the diagonal and side of a rectangle are not necessarily related by a factor of two.
Step-by-step explanation:
The question at hand involves a geometry concept related to parallelograms, and more specifically, rectangles. Correct answers must be determined based on the properties of rectangles, which are a type of parallelogram. In a rectangle, opposite sides are equal and all angles are 90 degrees.
Option a, which states m∠ABX + m∠CBX = 90°, seems to imply the sum of two angles at points that are not described within the context of a standard rectangle in geometry. Without additional context, such as the location of point X, this statement cannot be accurately validated.
Option b states m∠DXC = m∠BXC, which could be true if X is a point that allows for these angles to be reflections over the diagonal of the rectangle. However, again, without the exact location of point X, this cannot be confirmed.
Option c, which assumes 2AX = CD, does not necessarily hold true in a rectangle since the relationship between a diagonal (AX) and a side (CD) is not defined as such.