A) \[{{30}^{o}}\]
B) \[{{10}^{o}}\]
C) \[{{40}^{o}}\]
D) \[{{20}^{o}}\]
Correct Answer: A
Solution :
As, \[EF||AB\]and FA is transversal \[\therefore \]\[\angle EFA=\angle FAB\] (alternate interior angles) Also, \[CD||AB\]and CA is transversal \[\therefore \]\[\angle DCA+\angle BAC={{180}^{o}}\](co-interior angles) \[\Rightarrow \]\[{{145}^{o}}+\angle BAC={{180}^{o}}\Rightarrow \angle BAC={{35}^{o}}\] Now, \[\angle FAB=x+\angle CAB\] \[\Rightarrow \]\[{{65}^{o}}=x+{{35}^{o}}\Rightarrow x={{30}^{o}}\]
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