First, let's suppose the smallest angle is . Then the largest angle is . Since the triangle is acute-angled, , since must be an integer, and therefore a multiple of . This gives us that .
Next suppose that the third (middle-sized) angle of the triangle is . Using the angle-sum of a triangle, . The smallest possible value of is when is as large as possible; i.e. , and at this value the largest angle is .
If we make a bit smaller, say , then . But in this case , which is smaller than .
So the only solution is .