#BhatDC=150^@# so the reflex angle is #210^@#
Looking at the quad BGCD you have #100^@+210^@+B/2+C/2=360^@#
So #B/2+C/2=50^@#
Triangle BGF has #80^@+B/2+BhatFG=180^@#
#AhatFG = 80^@+B/2# (exterior angle on a triangle=sum of opposite two interior angles)
Triangle CEG has #80^@+C/2+ChatGE=180^@#
#AhatEG= 80^@+C/2# (exterior angle on a triangle=sum of opposite two interior angles)
So the quad AEGF has
#100^@+(80+B/2)+(80+C/2)+FhatAE=360^@#
#260^@+B/2+C/2+FhatAE=360^@#
#B/2+C/2+FhatAE=100#
But we know #B/2+C/2=50^@# so #FhatAE =50^@#
