Q. 15.0( 3 Votes )

Calculate the ang

Answer :


In Δ FBD


BFD + FBD + BDF = 180° (angle sum property)


BFD + 50 + 30 = 180°


BFD = 180° – 80° = 100°


Also, CFE = BFD =100° ( BFD and CFE are vertically


opp. Angle)


Since, EFD is a line


BFD + BFE = 180° (sum of angle on a straight line is 180°)


100 + BFE = 180°


BFE = 180° – 100° = 80°


Also, CFD = BFE = 80° ( BFE and CFD are vertically opp. Angle)


In Δ FBE


BFE + FBE + BEF = 180° (angle sum property)


FBE + 80 + 45 = 180°


FBE = 180° – 125° = 55°


Thus, DBE = FBD + FBE


DBE = 30 + 55 = 85°


In quad CDBE


DCE + DBE = 180° ( if all four vertices of a quadrilateral are


on circle then opposite angle are supplementary)


DCE + 85 = 180°


DCE = 180° – 85° = 95°


Also,


CBD = DEC = 30° ( angle in a same segment are equal)


CBE = CDE = 55° ( angle in a same segment are equal)


Thus, CDB = CDE + BDE


CDB = 55 + 50 = 105°


Thus, CEB = CED + BED


CEB = 30 + 45 = 75°


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