A) \[{{25}^{o}}\]
B) \[{{30}^{o}}\]
C) \[{{45}^{o}}\]
D) \[{{50}^{o}}\]
Correct Answer: D
Solution :
Through E, draw a line GEH Such that \[GH||AB||CD.\] As, \[GE||AB\]and AE is transversal \[\therefore \]\[\angle GEA=\angle EAB={{50}^{o}}\](alternate angles) Also, \[EH||CD\]and EC is transversal \[\therefore \]\[\angle HEC+\angle ECD={{180}^{o}}\](Co-interior angles) \[\Rightarrow \]\[\angle HEC={{80}^{o}}\] As GEH is a straight line \[\therefore \]\[\angle GEA+\angle AEC+\angle HEC={{180}^{o}}\] \[\Rightarrow \]\[{{50}^{o}}+x+{{80}^{o}}={{180}^{o}}\Rightarrow x={{180}^{o}}-{{130}^{o}}={{50}^{o}}\]You need to login to perform this action.
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