question_answer

The given figure shows three identical squares. Find x.            

A)  \[{{30}^{o}}\]                    

B)  \[{{27}^{o}}\]        

C)                     \[{{36}^{o}}\]                

D)         \[{{16}^{o}}\]                    

Correct Answer: B

Solution :

We have, ABCD, CEFG and CIHJ are all squares.             So, \[\angle 1+\angle 2+x={{90}^{o}}\]                  ???(i)             \[{{36}^{o}}+\angle 1+x={{90}^{o}}\]q                      ??.(ii)             \[x+\angle 2+{{27}^{o}}={{90}^{o}}\]            ??.(iii)             Adding (ii) and (iii), we get             \[{{36}^{o}}+x+{{27}^{o}}+(\angle A+\angle 2+x)={{180}^{o}}\]             \[\Rightarrow \] \[{{63}^{o}}+x+{{90}^{o}}={{180}^{o}}\]     (From (i))             \[\Rightarrow \] \[x={{180}^{o}}-{{153}^{o}}={{27}^{o}}\]