Sorry CPhill. Here is the full geometry question

Here's one method:

Find the center of the circle and call it "O"

Draw diameter F' D' through O  such that F'D' is parallel to FD

Draw F'E  and D'E .....

Now triangle F'ED'  is a right triangle with angle F'ED'  being the right angle [ since it intercepts the diameter ]

But the diameter in any circle is the greatest chord possible....so FD is shorter than F'D'

Therefore.....angle FED intercepts a lesser arc than angle F'ED'....therefore, angle FED < angle F'ED'

And since angle F'ED'  was shown to be right, then angle FED must be < 90°....therefore, acute

And similarly,  by drawing diameter F'E'  parallel to FE and  E'D' parallel to ED, we can show that angles FDE and EFD  are also acute

I drew the diagram but it is kind of onfusing on how you labeled the angles. Can you provide a diagram?

Here you go......it won't look exactly like the diagram, but it's close enough for you to get the idea

If you need extra explanation, let me know......