Question

$AB$ and $CD$ are the smallest and largest sides of a quadrilateral $ABCD$.

Out of $\angle B$ and $\angle D$, decide which is greater.

• A. $\angle B$ will be greater.
• B. Both the angles are equal.
• C. $\angle D$ will be greater.
• D. Cannot be determined.

Answer 1

Answer: (A)

The correct option is A $\angle B$ will be greater.

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 $\theta 1$ , $\theta 2$, $\theta 3$, $\theta 4$ as shown in figure.

Now in $\Delta ABD$,

$AB<AD$

$⟹\theta 2<\theta 1\to \left(1\right)$

Similarly in $\Delta BCD$,

$BC<CD$

$⟹\theta 4<\theta 3\to \left(2\right)$

Adding $\left(1\right)and\left(2\right)$,

$\theta 2+\theta 4<\theta 1+\theta 3$

which is nothing but,

$\angle D<\angle B$

Thus $\angle \left(B\right)$ will be greater.