How many non-similar triangles have angles whose degree measures are distinct positive integers in an arithmetic progression?

In this exercise we have to use the knowledge of triangles to calculate the degrees they have, in this way we can find that;

59, positive

Using arithmetic progression and triangle knowledge, we have:

Let the sum of the angle value will be:

The median term is equal to the average of the sum of all terms for a strange arithmetic progression of a strange number of terms:

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The answer is "59".

Step-by-step explanation:

Let the sum of the angle value is = 180

The median term is equal to the average of the sum of all terms for a strange arithmetic progression of a strange number of terms:

For all the smallest angle 1 is the minimal level possible as well as 59 is the highest possible, so there is 59 used as the numbers are different.