Question

AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of <B and <D decide which is greater.​

Answer 1

In the fig. ABCD is a quadrilateral with AB as the smallest side, and CD as the largest side.

We join the diagonal BD.

We label the angles as shown in the figure as θ1 , θ2, θ3, θ4 as shown in figure.

Now in ΔABD,

AB<AD

⟹θ2<θ1→(1)

Similarly in ΔBCD,

BC<CD

⟹θ4<θ3→(2)

Adding (1)and(2),

θ2+θ4<θ1+θ3

which is nothing but,

∠D<∠B

Thus ∠(B) will be greater