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