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, CD = 7 cm. 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

Step1: 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 = ${150}^{\circ }$

So, this construction is not possible.