A) \[{{42}^{o}}\]
B) \[{{52}^{o}}\]
C) \[{{128}^{o}}\]
D) \[{{134}^{o}}\]
Correct Answer: B
Solution :
\[\angle CDB+\angle BDE={{90}^{o}}\] (Angle of a rectangle) \[\Rightarrow \] \[{{48}^{o}}+\angle BDE={{90}^{o}}\] \[\Rightarrow \] \[\angle BDE={{90}^{o}}-{{48}^{o}}={{42}^{o}}\] In \[\Delta BED\] \[\angle EBD+\angle BDE+\angle BED={{180}^{o}}\] (Angle sum property) \[\Rightarrow \] \[{{86}^{o}}+{{42}^{o}}+\angle BED={{180}^{o}}\] \[\Rightarrow \] \[\angle BED={{180}^{o}}-({{86}^{o}}+{{42}^{o}})={{52}^{o}}\]
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