question_answer

In the given figure,\[AB||CD.\]Then the value of \[x\]is ____.        

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 \[\therefore \]\[\angle GEA+\angle AEC+\angle HEC={{180}^{o}}\] \[\Rightarrow \]\[{{50}^{o}}+x+{{80}^{o}}={{180}^{o}}\Rightarrow x={{180}^{o}}-{{130}^{o}}={{50}^{o}}\]