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David Cohen Just for you. Enjoy.
just use law of cos
find the measure of each angle in triangle ABD
you will get: <DAB=36.9, < ADB =119.94, <ABD=23.13
do same with triangle DBE and you get: <EDB=31.2, < DBE=55.7, <DEB=93.1
now you can find angles in triangle DEC
< CDE=180-(119.94+31.2)=28.9
< CED=180-93.1=86.9
since given DE=43, use angles above and side to calculate CD and CE