Recall that the diagonals of a square bisect each other, therefore:
[tex]BW=DW=6.[/tex]The diagonals are congruent, therefore:
[tex]AC\cong DB=2DW=2(6)=12.[/tex]To compute DA we use the fact that the figure is a square:
[tex]DA=DC=8.5.[/tex]Now, we know that the angles at the vertices are right angles, therefore:
[tex]m\angle ABC=90.[/tex]To determine the measure of angles ABD, and DCA we use the trigonometric function sine:
[tex]\begin{gathered} sin(\angle ABD)=\frac{DA}{DB}=\frac{\sqrt{287}}{2(12)}, \\ sin(\angle DCA)=\frac{DA}{CA}=\frac{\sqrt{287}}{2(12)}. \end{gathered}[/tex]Therefore:
[tex]m\angle ABD=m\angle DCA\approx45^{\circ}.[/tex]Finally, to determine the measure of angle DWA, we use the fact that the figure is a square, therefore the diagonals bisect each other at 90° angles.