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AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of \angleB and \angleD decide which is greater

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ABCD is quadrilateral

AB and CD are smallest and greatest side of ABCD.

Join BD

In \triangleBCD

DC < BC                                 (\because CD is Greatest side)

\angleCBD > \angleBDC          (Angle opposite to greater side is greater)                …(i)

In \triangleABD

AD > AB                                 (AB is the smallest side)

\angleABD > \angleADB         (Angle opposite to greater side is greater)                …(ii)

Adding (i) and (ii)

\angleCBD + \angleABD > \angleBDC + \angleADB

\angleABC >\angleADC

Hence \angleB is greater.

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