The first step is to find #angleC#.
We know that #angleA = 30# and #angleB = 90#. Since all triangles have angles that add up to 180,
#angleC = 180 - 30 - 90#
#angleC = 60#
We can use this to complete the next step: finding #angleCEB# (this is complementary with #angleCED#, so we'll be able to find #angleCED# by subtracting #angleCEB# from 90).
We can do this by taking #triangleCEB# as its own triangle. #angleB# is still 90. #angleECB# is #angleC-:2#, since #bar(CE)# bisects #angleC#. So #angleECB = 30#.
#angleCEB = 180 - 90- 30#
#angleCEB = 60#
#angleCED = 90 - 60#
#color(red)(angleCED = 30)#
