Question

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

• A. $\angle B>\angle D$
• B. $\angle B<\angle D$
• C. $\angle B=\angle D$
• D. cannot be determined

Answer 1

The correct option is A $\angle B>\angle D$



Join B and D.
Given, AB = 2 cm, AD = 4 cm, BC = 3 cm and CD = 5 cm.
In a triangle, the angle opposite to longer side is larger.
$\therefore$ In $\Delta BAD$, $\angle 1>\angle 3$ $\cdots$(i)
$\therefore$ In $\Delta BCD$, $\angle 2>\angle 4$ $\cdots$(ii)
On adding (i) and (ii),
$\angle 1+\angle 2>\angle 3+\angle 4$
$⟹\angle B>\angle D$.