#### Question

The sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E; the sides DA and CB are produced to meet at F. If ∠BEC = 42° and ∠BAD = 98°; Calculate :

(i) ∠AFB (ii) ∠ADC

#### Solution

By angle sum property of ∆ADE,

∠ADC = 180° - 98° - 42° = 40°

Also, ∠ADC + ∠ABC =180°

(pair of opposite angles in a cyclic quadrilateral are supplementary)

∴ ∠ABC = 180° - 40° = 140°

Also, ∠BAF = 180° - ∠BAD = 180° - 98° = 82°

∴ ∠ABC = ∠AFB + ∠BAF

(Exterior angle of a ∆ is equal to the sum of pair of interior opposite angles)

⇒ ∠AFB =140° - 82° = 58°

Thus, ∠AFB = 58° and ∠ADC = 40°

Is there an error in this question or solution?

Solution The Sides Ab and Dc of a Cyclic Quadrilateral Abcd Are Produced to Meet at E; the Sides Da and Cb Are Produced to Meet at F. If ∠Bec = 42° and ∠Bad = 98°; Calculate : (I) ∠Afb (Ii) ∠Adc Concept: Chord Properties - Chords Equidistant from the Center Are Equal (Without Proof).