Question 19 If AB and CD are the smallest and largest sides of a quadrilateral ABCD, out of ∠B and ∠D decide which is greater.
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Solution
Construction: Join BD. Now, in △ABD,AD>AB [since, AB is the smallest side in ABCD] ⇒∠1>∠3 [angle opposite to larger side is greater]...(i) In ΔBCD,CD>BC [since, CD is the largest side in ABCD] ⇒∠2>∠4 [angle opposite to larger side is greater] ...(ii) On adding Eqs. (i) and (ii), we get ∠1+∠2>∠3+∠4 Hence, ∠B>∠D.