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, 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

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 = ${150}^{\circ }$

The sum of angles in a triangle should always be equal to ${180}^{\circ }$. So, this construction is not possible.