You have seen that the value chosen for AE determines the value of DE + EC. One also says that DE + EC is a function of AE. Letting x stand for AE (and 30 - x for EB), write a formula for this function. Then enter this formula into your calculator, graph it and find the value of x that produces the shortest path from D to C through E. Draw an accurate picture of this path and make a conjecture about angles AED and BEC.

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