A) \[{{111}^{o}}\]
B) \[{{112}^{o}}\]
C) \[{{113}^{o}}\]
D) \[{{114}^{o}}\]
Correct Answer: B
Solution :
Since, \[AB||CD\] \[\therefore \] \[\angle CAB+\angle DCA={{180}^{o}}\] (Co-interior angles) \[\therefore \] \[{{22}^{o}}+\angle DCA={{180}^{o}}\] \[\Rightarrow \] \[\angle DCA={{180}^{o}}-{{22}^{o}}={{158}^{o}}\] Also, \[\angle ECD+\angle DCA+\angle y={{360}^{o}}\] (Angles about a point) \[\Rightarrow \] \[{{90}^{o}}+{{158}^{o}}+\angle y={{360}^{o}}\] \[\Rightarrow \]\[\angle y={{360}^{o}}-({{90}^{o}}+{{158}^{o}})\] \[\Rightarrow \] \[\angle y={{360}^{o}}-{{248}^{o}}={{112}^{o}}\]
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