question_answer

In the given figure, \[AB||CD,\]find \[\angle ODC.\]

A) \[{{70}^{o}}\]

B) \[{{80}^{o}}\]

C)        \[{{90}^{o}}\]

D)        \[{{34}^{o}}\]

Correct Answer: C

Solution :

It is given that,\[AB||CD\] Draw a line OP such that\[OP||AB\] \[\therefore \] \[OP||CD\] Now, \[\angle ABO={{118}^{o}}\] \[\angle BOD={{152}^{o}}\]                                 (given) Since, \[OP||AB\] \[\Rightarrow \]\[\angle ABO+\angle BOP={{180}^{o}}\](co-interior angles) \[\Rightarrow \]\[\angle BOP={{62}^{o}}\] And \[\angle BOP+\angle POD=\angle BOD\] \[\Rightarrow \]\[{{62}^{o}}+\angle POD={{152}^{o}}\Rightarrow \angle POD={{90}^{o}}\] Now, \[PO||CD\] \[\Rightarrow \]\[\angle POD+\angle ODC={{180}^{o}}\] \[\Rightarrow \]\[\angle ODC={{180}^{o}}-{{90}^{o}}\Rightarrow \angle ODC={{90}^{o}}\]