Question

Is it possible to construct a unique quadrilateral ABCD with AB = 4cm, AD = 6 cm, $\angle ABC=60°$ , $\angle DAB=75°$, $\angle ADC=85°$? If yes, construct it and find $\angle BCD$.

• A. No, it is impossible
• B. yes, ${130}^{\circ }$
• C. yes, ${140}^{\circ }$
• D. yes, ${150}^{\circ }$

Answer 1

The correct option is C

yes, ${140}^{\circ }$

We have 5 measurements. So, we can, of course, construct a quadrilateral.

Step1: Draw AB = 4 cm

Step 2: Draw $\angle DAB=75°$and mark AD = 6 cm on it

Step 3: At D, draw an angle of ${85}^{\circ }$ ($\angle ADC$) and extend the line along $\angle ADC$

Step 4: Draw ${60}^{\circ }$ at B($\angle ABC$) and extend the line along $\angle ABC$ such that it intersects the line extended along $\angle ADC$. Mark the point of intersection as C.

Step 5: Join all the points A,B,C and D. Measure $\angle$BCD. It is equal to ${140}^{\circ }$ _.

Alternate :

BCD = ${360}^{\circ }$ - ($\angle$ABC+ $\angle$DAB+ $\angle$ADC)

= ${360}^{\circ }$ - (${60}^{\circ }$ +${75}^{\circ }$ +${85}^{\circ }$)= ${360}^{\circ }$ -${220}^{\circ }$ = ${140}^{\circ }$