---
id: 5900f41e1000cf542c50ff30
title: 'Problem 177: Integer angled Quadrilaterals'
challengeType: 5
forumTopicId: 301812
dashedName: problem-177-integer-angled-quadrilaterals
---

# --description--

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.

<img class="img-responsive center-block" alt="convex quadrilateral ABCD, with diagonals AC and BD" src="https://cdn.freecodecamp.org/curriculum/project-euler/integer-angled-quadrilaterals.gif" style="background-color: white; padding: 10px;">

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.

# --hints--

`integerAngledQuadrilaterals()` should return `129325`.

```js
assert.strictEqual(integerAngledQuadrilaterals(), 129325);
```

# --seed--

## --seed-contents--

```js
function integerAngledQuadrilaterals() {

  return true;
}

integerAngledQuadrilaterals();
```

# --solutions--

```js
// solution required
```
