a) The side length of a square ABCD is 4. P and Q are points on the sides AB and BC respectively such that BP = 1 and BQ = 3. Prove that angle PAQ + angle PDQ + angle PCQ = 90 degrees.

b) In a quadrilateral ABCD, there is a point X on the side BC such that XA and XD are the angle bisectors of angle BAD and angle CDA respectively. Prove that if AB = BX, then BC = AB + CD.