question_answer

In the given figure, \[AB||CD.\]Find the value of \[x.\]

A) \[{{189}^{o}}\]

B) \[{{215}^{o}}\]

C)        \[{{285}^{o}}\]

D)        \[{{280}^{o}}\]

Correct Answer: C

Solution :

Draw \[EO||AB||CD\] So, \[\angle 1+\angle 2=x\] As \[EO||AB\]and OB is transversal \[\therefore \]\[\angle 1+\angle ABO={{180}^{o}}\](co-interior angles) \[\Rightarrow \]\[\angle 1+{{40}^{o}}={{180}^{o}}\Rightarrow \angle 1={{140}^{o}}\] Also, and DO is transversal \[\therefore \]\[\angle 2+\angle CDO={{180}^{o}}\](co-interior angles) \[\Rightarrow \]\[\angle 2+{{35}^{o}}={{180}^{o}}\Rightarrow \angle 2={{145}^{o}}\] \[\therefore \]\[\angle 1+\angle 2={{140}^{o}}+{{145}^{o}}={{285}^{o}}\] \[\therefore \]\[x={{285}^{o}}\]                      \[(\because \,x=\angle 1+\angle 2)\]