Question

In the quadrilateral ABCD, AB = 2 cm, BC = 3 cm, CD = 5 cm and AD = 4 cm, then relation between $\angle B$ and $\angle D$ is?

• A. $\angle B>\angle D$
• B. $\angle B<\angle D$
• C. $\angle B=\angle D$
• D. None of these

Answer 1

The correct option is A

$\angle B>\angle D$

Join B and D.
In a triangle, angle opposite to longer side is greater than the angle opposite to shorter side.
$\therefore In\Delta BAD,\angle 1>\angle 3$ $\dots$(i)
$\therefore In\Delta BCD,\angle 2>\angle 4$ $\dots$(ii)
On adding (i) and (ii)
$\angle 1+\angle 2>\angle 3+\angle 4$
$\angle B>\angle D$