Question

Whether is it possible to construct a unique quadrilateral ABCD with AB = 6cm, AD = 7cm, $\angle$ABC = ${30}^{\circ }$ , $\angle$DAB = ${60}^{\circ }$,

$\angle$ADC = ${80}^{\circ }$ ? If yes, construct it and find $\angle$BCD.

• A. No, it is impossible
• B. Yes, 130^o
• C. Yes, 190^o
• D. Yes, 140^o

Answer 1

The correct option is C

Yes, 190^o

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

($\angle$​BCD = 360^o - (($\angle$​ABC+ ($\angle$​DAB+ ($\angle$​ADC)

= 360${}^{\circ }$- (30${}^{\circ }$​ +60${}^{\circ }$​ +80${}^{\circ }$​⁾

= 360${}^{\circ }$​ - 170${}^{\circ }$​ = 190${}^{\circ }$