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.
Answer:
[tex]\begin{gathered} BW=6, \\ AC=12, \\ DA=8.5, \\ m\angle DWA=90^{\circ}, \\ m\angle ABC=90^{\circ}, \\ m\angle ABD=45^{\circ}, \\ m\angle DCA=45^{\circ}. \end{gathered}[/tex]
