In the diagram, triangle ABE, triangle BCE and triangle CDE are right-angled, with angle AEB = angle BEC = angle CED = 50 degrees, and AE=24. Find the perimeter of quadrilateral ABCD.

In the diagram, triangle ABE, triangle BCE, and triangle CDE are right-angled, with angle AEB = angle BEC = angle CED = 60 degrees, and AE=24. Find the perimeter of quadrilateral ABCD.