Question

Is it possible to construct a unique quadrilateral ABCD with AB = 4 cm, AD = 6 cm, $\angle$ABC = ${60}^{\circ }$, $\angle$DAB = ${75}^{\circ }$,

$\angle$ADC = ${85}^{\circ }$? If yes, construct it and find $\angle$BCD.

• A. No, it is impossible
• B. yes,
• C. yes,
• D. yes,

Answer 1

The correct option is C

yes,

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

Step1: Draw AB = 4 cm

Step 2: Draw $\angle$DAB = ${75}^{\circ }$ 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:

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

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