For these kinds of problems, there are a couple of relationships worth remembering.
• an angle whose vertex is on the circle intercepts an arc that is double its measure
• the angle where two chords cross will have a measure that is the averagle of the measures of the intercepted arcs. (G is the average of BCD and AE)
From these relationships, you know arc BAD = 2*119° = 238°, so arc BCD is
.. 360° -238° = 122°
And the sum of AE and BCD will be 2*G.
.. 2*90° - 122° +AE
.. AE = 58°