Question

$\Delta BEF$ and $\Delta FED$ are two isosceles triangles in the square ABCD.

What is the measure of $\angle FBE$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$Given,\angle AFB={70}^{\circ }$
Also, $\Delta \left(BFE\right)$ is an isosceles triangle and $\Delta \left(DFE\right)$ is a right isosceles triangle,
$so2\times \left(\angle DFE\right)={180}^{\circ }-{90}^{\circ }={90}^{\circ }or,\left(\angle DFE\right)={45}^{\circ }now,as\left(\angle DFE\right)+\left(\angle BFE\right)+\left(\angle BFA\right)={180}^{\circ }so,\left(\angle BFE\right)={180}^{\circ }-{70}^{\circ }-{45}^{\circ }={65}^{\circ }and,\left(\angle FBE\right)={180}^{\circ }-2\times \left({65}^{\circ }\right)=50$