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in this quadrilateral angles(a+b+c+d=360°) so,a+b=360°-(c+d)....1 in triangle abp angle bap=a/2 because it is the bisector of angle a angle abp=b/2 because it is a bisector of angle b so, a/2+b/2+angle apb=180° (Δs property).....2 now putting he value from 1 to 2 360°-(c+d)/2+angle apb=180° 360°/2+(-c-d/2)+angle apb=180° 180°+(-c-d/2)+angle apb=180° angle apb=c+d/2 now putting the value of c and d apb=100°+60°/2 apb=160°/2 apb=80°