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Sides AB and DC of cyclic quadrilateral ABCD are produced to meet at E, and sides AD and BCare produced to meet at F. If
∠BAD=102∘ and ∠BEC=38∘ then the difference between ∠ADC and ∠AFB
is:
21∘
31∘
22∘
23∘
In ΔADE, ∠ADE=180 − (∠AED + ∠EAD) = 180 − (38 + 102) = 40\degree ⇒∠ADC = 40\degree square ABCD is a cyclic quadrilateral. ∴∠DCB + ∠DAB=180 ⇒∠DCB = 180 − ∠DAB ∠DCB = 180 − 102 ∠DCB = 78\degree In ΔDFC, ∠DFC=180 - (∠FDC+∠FCD) ∠DFC = 180 − (40 + 78) ∠DFC = 180 − 118 ∠DFC = 62\degree ∠AFB = ∠DFC = 62\degree. Difference between ∠BAD and ∠AFB = 62 - 40 = 22\degree
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