How many non-[similar](https://artofproblemsolving.com/wiki/index.php/Similar) triangles have angles whose degree measures are distinct positive integers in [arithmetic progression](https://artofproblemsolving.com/wiki/index.php/Arithmetic_progression)? 
$\textbf{(A) } 0\qquad\textbf{(B) } 1\qquad\textbf{(C) } 59\qquad\textbf{(D) } 89\qquad\textbf{(E) } 178\qquad$
The sum of the angles of a triangle is $180$ degrees. For an arithmetic progression with an odd number of terms, the middle term is equal to the average of the sum of all of the terms, making it $\frac{180}{3} = 60$ degrees. The minimum possible value for the smallest angle is $1$ and the highest possible is $59$ (since the numbers are distinct), so there are $\boxed{\textbf{(C) }59}$ possibilities.