Sides AB and DC of a cyclic quardrilateral ABCD are produced to meet at E and sides AD and BC are produced to meet at F. If ∠ADC = 80° and ∠BEC = 54°, then the measure of ∠AFB is.

34°

∠ADC = 80°

∠ABC = 180° - ∠ADC = 180° - 80° = 100°  (Cyclic quadrilateral property)

In Δ ADE:

∠DAB = 180° -  (∠ADE + ∠DEA)

         = 180° - 134° = 46°

Hence, In Δ ABF:  

∠AFB = 180° -  (∠BAF + ∠ABF)

         = 180° - 146° = 34°