Let $ABCD$ be a convex quadrilateral, with diagonals $AC$ and $BD$. At each vertex the diagonal makes an angle with each of the two sides, creating eight corner angles.

For example, at vertex $A$, the two angles are $CAD$, $CAB$.

We call such a quadrilateral for which all eight corner angles have integer values when measured in degrees an "integer angled quadrilateral". An example of an integer angled quadrilateral is a square, where all eight corner angles are ${45}^{\circ }$. Another example is given by $DAC={20}^{\circ }$, $BAC={60}^{\circ }$, $ABD={50}^{\circ }$, $CBD={30}^{\circ }$, $BCA={40}^{\circ }$, $DCA={30}^{\circ }$, $CDB={80}^{\circ }$, $ADB={50}^{\circ }$.

What is the total number of non-similar integer angled quadrilaterals?

Note: In your calculations you may assume that a calculated angle is integral if it is within a tolerance of ${10}^{-9}$ of an integer value.