Question

In the figure given, equilateral triangle $EBC$ surmounts square $ABCD$. Find angle $BED$ represented by $x$.

Answer 1

REF.Image

$△BEC$ is an equilateral $△le$

$\Rightarrow BE=EC=BC$

But $BC=CD(ABCD$ is a square)

$\Rightarrow EC=CD\Rightarrow \angle CED=\angle CDE$

In $△ECD,\angle CED+\angle CDE+90+60=180$

$\Rightarrow 2\angle CED=30\Rightarrow \angle CED={15}^{\circ }$

$\angle BEC={60}^{\circ }\Rightarrow x=60-15=45$