Question

Is 78 degrees the correct answer?

Answer 1

We have 2 intersecting chords so:
Whenever 2 chords intersect,
Angle AED = Angle BEC = 66 degrees
66 degrees = .5 * (arc AD + Arc BC)
66 degrees = .5 * (arc AD + Arc BC)
66 degrees = .5 * (54 + Arc BC)
66 degrees -27 = .5 Arc BC
39 degrees = .5 Arc BC
Arc BC = 78 degrees
So, you are correct Ranya2

Source:
http://www.1728.org/circangl.htm

Answer 2

Yes as long as the sum of all the numbers equals 360°