question_answer

In the given figure, \[x\]and y are____.         

A) \[x=70{}^\circ ,y={{37}^{o}}\]     

B)        \[~x=37{}^\circ ,\,y=70{}^\circ \] 

C)        \[~x+y=117{}^\circ \]      

D)        \[x-y=100{}^\circ \]          

Correct Answer: B

Solution :

In\[\Delta ABD\]and \[\Delta \Alpha CD\] \[AB=AC\]                                [Given] \[BD=CD\]                                            [Given] \[AD=AD\]                                [Common] \[\Rightarrow \]\[\Delta ABD\cong \Delta ACD\] [By SSS Rule] \[\Rightarrow \]\[\angle BDA=\angle CDA\] \[\Rightarrow \]\[y={{70}^{o}}\] Similarly, \[x={{37}^{o}}\]