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.
Answer & explanation
Correct answer: option 3
∠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°