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 = 75º and ∠BEC = 52º, then the measure of ∠AFB is :
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 22º
In the triangle ADE the sum of all angles is 180º
⇒ EAD = 180º - (75º + 52º)
⇒ EAD = 53º
As the sum of opposite angles of the cyclic quadrilateral is 180º and the sum of the angles on a line is 180º.
⇒ EAD = DCF = 53º
⇒ CDF = 180º - 75º
⇒ 105º
⇒ AFB = 180º - (105º + 53º)
⇒ 22º