Question

Question 19
If AB and CD are the smallest and largest sides of a quadrilateral ABCD, out of $\angle B$ and $\angle D$ decide which is greater.

Answer 1

Construction: Join BD.
Now, in $△ABD,AD>AB$ [since, AB is the smallest side in ABCD]
$\Rightarrow \angle 1>\angle 3$ [angle opposite to larger side is greater]...(i)
In $\Delta BCD,CD>BC$ [since, CD is the largest side in ABCD]
$\Rightarrow \angle 2>\angle 4$ [angle opposite to larger side is greater] ...(ii)
On adding Eqs. (i) and (ii), we get
$\angle 1+\angle 2>\angle 3+\angle 4$
Hence, $\angle B>\angle D$.