# Problem 177: Integer angled Quadrilaterals

![graphic](img177.gif)

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°. Another example is given
by DAC = 20°, BAC = 60°, ABD = 50°, CBD = 30°, BCA = 40°, DCA = 30°, CDB
= 80°, ADB = 50°. 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.