Question

In the figure, not drawn to scale, $ACDF$ is a rectangle and $BDE$ is a triangle. Find $\angle BED$

• A. ${42}^o$
• B. ${52}^o$
• C. ${128}^o$
• D. ${134}^o$

Answer 1

The correct option is B ${52}^o$

$\angle CDB+\angle BDE={90}^o$ (Angle of rectangle)
$\Rightarrow {48}^o+\angle BDE={90}^o$
$\Rightarrow \angle BDE={90}^o-{48}^o={42}^o$
In $△BED,\angle EBD+\angle BDE+\angle BED={180}^o$ (Angle sum property)
$\Rightarrow {86}^o+{42}^o+\angle BED={180}^o$
$\Rightarrow \angle BED={180}^o-({86}^o+{42}^o)={52}^o$