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 = 5cm and CD = 7cm. Can we construct this parallelogram?

• A. Yes, of course
• B. With 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= ${15}^{\circ }$ ......... (1) (Alternate interior angles)

In $△$ ABC,

$\angle$A+ $\angle$B+ $\angle$C must be ${180}^{\circ }$

$\angle$A+ $\angle$B+ $\angle$C=${25}^{\circ }$+${110}^{\circ }$+${15}^{\circ }$ (from (1))

$\angle$A+ $\angle$B+ $\angle$C= ${150}^{\circ }$ $\ne$ ${180}^{\circ }$.

So, this construction is not possible.