Question

We have a parallelogram ABCD with AC and BD as diagonals. In Parallelogram ABCD, $\angle ABC={110}^{\circ }$, $\angle DAC={15}^{\circ }$, $\angle CAB={25}^{\circ }$, AB = 5 cm and CD = 7 cm. Can we construct this parallelogram?

• A. Yes, of course.
• B. With $\angle$ADC, yes.
• C. With AC, yes.
• D. No, it is impossible.

Answer 1

The correct option is D

No, it is impossible.

Draw rough diagram of the parallelogram ABCD.

Here, $\angle$DAC = $\angle$ACB= ${15}^{\circ }$ $\dots$ (1) $\because \text{(Alternate interior angles)}$
In $△$ ABC,
$\angle A$+ $\angle B$ + $\angle C$ must be ${180}^{\circ }$
$\angle A$+ $\angle B$ + $\angle C$ = ${25}^{\circ }$+ ${110}^{\circ }$+ ${15}^{\circ }$ $\dots$from (1)
$\angle A$+ $\angle B$ + $\angle C$ = ${150}^{\circ }$
So, this construction is not possible.