In △ABD
AB>AD (AB is the longest side of quadrilateral ABCD)
∠BDA>∠DBA (Angle opposite to the greater side is
greater) ... (1)
In △BDC
BC>CD (CD is the smallest side of quadrilateral ABCD)
=>∠BDC>∠CBD (Angle opposite to the
greater side is greater) ... (2)
On adding equations (1) and (2), we obtain
∠BDC+∠BDA>∠DBA+∠CBD
=>∠D>∠B