Q24.

In the above figure (not to scale )  AB ,   BC , CF , DE  and  FE  are chords of the circle. If  ABC = 100° and ​ FED = 110°, then ​ FPA = 

   (a) 20°                                                           (b) 30­°

   (c) 40°                                                           (d) 70°

Dear Student ,
 
Please find below the solution to the asked query :




AFED and ABCF are cyclic quadrilaterals as their all vertices lies on the circle.In cyclic quadrilateral AFED,FED+FAD=180°         Opposite angles of cyclic quadrilateral are supplementary 110°+FAD=180°FAD=70°FAP=70°In cyclic quadrilateral ABCF,ABC+AFC=180°         Opposite angles of cyclic quadrilateral are supplementary 100°+AFC=180°AFC=80° AFP=80°Now, In AFP , using angle sum propertyFAP+AFP+FPA=180°70°+80°+FPA=180°150°+FPA=180°FPA=30°Correct option is B.
 
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