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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 - ICSE Class 10 - Mathematics

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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°

 

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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).
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