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<h2>Integer angled Quadrilaterals.</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 177</h3><span style="width:300px;color:#666;">Published on Friday, 11th January 2008, 09:00 pm; Solved by 676</span></div>
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<p>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.</p>
<p style="margin-left:180px;"><img src="project/images/p_177_quad.gif" alt="" /></p>
<p>For example, at vertex A, the two angles are CAD, CAB.</p>
<p>We call such a quadrilateral for which all eight corner angles have integer values when measured in degrees an &quot;integer angled quadrilateral&quot;. An example of an integer angled quadrilateral is a square, where all eight corner angles are 45&deg;. Another example is given by DAC = 20&deg;, BAC = 60&deg;, ABD = 50&deg;, CBD = 30&deg;, BCA = 40&deg;, DCA = 30&deg;, CDB = 80&deg;, ADB = 50&deg;.</p>
<p>What is the total number of non-similar integer angled quadrilaterals?</p>
<p>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.</p>
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