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