n circle A shown below, m Arc BC is 61° and m Arc EF is 76°: Points B, C, E, F lie on Circle A. Lines BE and CF pass through point D creating angle EDF. Measure of arc BC is 61 degrees and What is m∠FDE?

Here is the solution:

m<FDE = 1/2( Arc BC + Arc 76) 
m<FDE = 1/2 (61° + 76°) 
m<FDE = 137/2 = 68.5°

So the answer is 68.5°