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    Question

    Find the value of X in the given figure:

    src="http://ixambee.com/questionimage/ssc/SSC-MT18-E-68.jpg" alt="" width="628" height="427" />
    A 74˚ Correct Answer Incorrect Answer
    B 149˚ Correct Answer Incorrect Answer
    C 64˚ Correct Answer Incorrect Answer
    D 58˚ Correct Answer Incorrect Answer

    Solution

    In the given figure ∠ABF + ∠CBF = 180˚ (Angles in a straight line) 75˚ + ∠CBF = 180˚ ∠CBF = 105˚ Now, in ∆CBE ∠CBE + ∠BCE + ∠CEB = 180˚ 105˚ + ∠BCE + 44˚ = 180˚ ∠BCE = 180˚ - (105˚+ 44˚) ∠BCE = 31˚ ∠BCE + ∠DFB = 180˚ (Sum of opposite sides of Cyclic Quadrilateral) ∠DFB = 180˚ - 31˚ = 149˚ ∠DFB + ∠AFB = 180˚ ∠AFB = 180˚ - 149˚ = 31˚ In ∆ABF ∠AFB + ∠FAB + ∠AFB = 180˚ ∠FAB = 180˚-(75˚+31˚) = 74˚

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