A) \[{{79}^{o}},\,\,{{47}^{o}}\]
B) \[{{89}^{o}},\,\,{{37}^{o}}\]
C) \[{{89}^{o}},\,\,{{47}^{o}}\]
D) \[{{79}^{o}},\,\,{{37}^{o}}\]
Correct Answer: B
Solution :
In \[\Delta \Alpha \Epsilon \Beta ,\angle ABE+\angle BEA+BAE={{180}^{o}}\] \[\Rightarrow \]\[{{35}^{o}}+\angle BEA+{{54}^{o}}={{180}^{o}}\] \[\Rightarrow \]\[\angle BEA={{91}^{o}}\] Now, \[\angle AFD+\angle DEA={{180}^{o}}\] (opposite angles of cyclic quadrilateral) \[\Rightarrow \]\[x+{{91}^{o}}={{180}^{o}}\Rightarrow x={{89}^{o}}\] In \[\Delta AFC,\angle AFC+\angle FCA+\angle CAF={{180}^{o}}\] \[\Rightarrow \]\[{{89}^{o}}+y+{{54}^{o}}={{180}^{o}}\Rightarrow y={{37}^{o}}\]
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