61 lines
1.4 KiB
Markdown
61 lines
1.4 KiB
Markdown
---
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id: 5900f41e1000cf542c50ff30
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challengeType: 5
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title: 'Problem 177: Integer angled Quadrilaterals'
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---
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## Description
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<section id='description'>
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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.
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For example, at vertex A, the two angles are CAD, CAB.
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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°.
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What is the total number of non-similar integer angled quadrilaterals?
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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.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler177()</code> should return 129325.
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testString: assert.strictEqual(euler177(), 129325, '<code>euler177()</code> should return 129325.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler177() {
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// Good luck!
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return true;
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}
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euler177();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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