Given the three angles of a triangle, only ONE distinct triangle can be formed. We can use dilation to scale up or scale down and make an infinite number of triangle, based on this set of angles, all such triangles will be similar to each other.
Hope this helps.
There are infinitely many triangles that can be solved when only given 3 angles of the triangle and nothing more. With the angles we know how the triangle would look: obtuse, acute, right... but not how big nor how small it is. You can have many different length combinations for a triangle and still have the same angles in the triangles.
If you know all the 3 angles (make sure they sum to 180), then you can form an Infinite number of triangles.
Why I am saying this is, we know only angles of the triangle, but not the side lengths .
So, there is a possibility to form as many number of triangles with same 3 angles, which make all those set of triangles as similar triangles.
But if you also know the side lengths, then you can only form 1 Triangle