ABCD is a cyclic quadrilateral, Sides AB and DC, when…

ABCD is a cyclic quadrilateral, Sides AB and DC, when produced, meet at E and sides AD and BC when produced, meet at F. If $\angle$ ADC = 76º and $\angle$ AED = 55º, then $\angle$ AFB is equal to:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 27º

In $\triangle$ AED,

$\angle$ AED + $\angle$ ADE + $\angle$ DAE = 180

$\angle$ DAE = 180 - 76 - 55 = 49°.

$\angle$ ADC + $\angle$ ABC = 180

$\angle$ ABC = 180 - 76 = 104°.

In $\triangle$ ABF,

$\angle$ BAF + $\angle$ ABF + $\angle$ AFB = 180

$\angle$ AFB = 180 - 104 - 49 = 27°.

SSC CGL 2022 PYQ — Question 83