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Question
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
Given: In quadrilateral ABCD, AB is the smallest and CD is the largest side
To find: ∠B > ∠D or ∠D > ∠B.
Construction: Join BD.
Now, in ΔABD, 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 equations (i) and (ii), we get
∠1 + ∠2 > ∠3 + ∠4
Hence, ∠B > ∠D
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