find $m\\angle d$.\n$m\\angle d = \\square^\\circ$\nsubmit

Explanation:

Step1: Identify given sides

In right $\triangle DEF$, $\angle E=90^\circ$, $FE=2$, $FD=2\sqrt{2}$.

Step2: Use sine for $\angle D$

$\sin(\angle D)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{FE}{FD}$ $\sin(\angle D)=\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}$

Step3: Find $\angle D$ value

We know $\sin(45^\circ)=\frac{\sqrt{2}}{2}$, so $\angle D=45^\circ$.

Answer:

$45$