yaworsw/euler-manager

---
:id: 177
:name: Integer angled Quadrilaterals
:url: https://projecteuler.net/problem=177
:content: |+
  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.

  ![]({{ images_dir }}/p177_quad.gif)

  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<sup>-9</sup> of an integer value.