question_answer

The sides BA and DC of a quadrilateral ABCD are produced as shown in figure, them a + b = ?

A) \[x+2y\]                       

B) \[2x+y\]

C) \[2(x+y)\]                     

D) \[(x+y)\]

Correct Answer: D

Solution :

Join BD In \[\Delta \,ABD,\]             \[\angle ABD+\angle ADB=b\]                 ?.(i) In \[\Delta \,CBD,\]             \[\angle CBD+\angle CDB=a\]                 ?(ii) Adding Eqs. (i) and (ii), \[\angle ABD+\angle CBD+\angle ADB+\angle CDB\] \[=a+b\] \[\Rightarrow \]   \[x+y=a+b\]