Question

Given below are the steps of construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, $\angle A={75}^{\circ },\angle B={105}^{\circ }$ and $\angle C={120}^{\circ }$. Which of the following options is the wrong step?
1:- Draw AB = 3.5 cm.
2:- Draw $\angle DAB={75}^{\circ },\angle ABC={105}^{\circ }$ at B.
3:- Draw BC = 6.5 cm.
4:- At D draw $\angle ADC={120}^{\circ }$.

• A. 3
• B. 2
• C. 4
• D. 1

Answer 1

The correct option is C 4

The wrong step is 4.
Sum of all angles of a quadrilateral add upto ${360}^{\circ }$.
$\angle A$,$\angle B$ and $\angle C$ add upto ${300}^{\circ }$.
Thus the value of $\angle D$ should be ${60}^{\circ }$.
But it is ${120}^{\circ }$ and thus does not form a quadrilateral.