Sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E, and sides AD and BC are produced to meet at F. If ∠ADC = 75°, and ∠BEC = 52°, then the difference between ∠BAD and ∠AFB is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 31°
In triangle ADE the sum of all the angles is 180°
⇒ 75° + 52° + ∠DAE = 180°
⇒ ∠DAE = 53°
In the cyclic quadrilateral, the sum of opposite angles is 180°.
⇒ ∠ADE + ∠ABC = 180°
⇒ ∠ABC = 105°
In the triangle ABF
⇒ 53° + 105° + ∠AFB = 180°
⇒ ∠AFB = 22°
The difference between ∠BAD and ∠AFB = 53° - 22° = 31°