Question

A playground is in the form of a rectangle FATE. Two players are standing at the points F and B. Where EF=EB Find the values of x and y.

Answer 1

Given to us $EB=EF$

Therefore. $\angle EBF=\angle EFB$

Now in a right angle triangle , sum of all angles $={180}^{\circ }$

Therefore $\angle EBF+\angle EFB+\angle BEF={180}^{\circ }$. (and $\angle BEF={90}^{\circ }$)

$(2\times \angle EBF)+{90}^{\circ }={180}^{\circ }$

Therefore $\angle EBF={45}^{\circ }=\angle EFB$

Therefore $\angle EFB+\angle y={90}^{\circ }$. (Right angle)

$y={45}^{\circ }$. (because $\angle EFB={45}^{\circ }$)

Similarly $\angle EBF+\angle x={180}^{\circ }.$ (Linear angle )

${45}^{\circ }+\angle x={180}^{\circ }$

$\angle x={135}^{\circ }$