the number of different triangles How many  different  triangles in which the measurement of the interior angles in degree is representing natural numbers in arithmetic sequence 

I assume you want to know how many triangles up to similarity there are (so side lengths don't matter). I further assume you mean that the interior angles are (in degrees) $n,n+m,n+2m,$ with each a natural number. In particular, we need $n$ to be a natural number, and $m$ to be (without loss of generality) a non-negative integer (unless you require the angles be distinct, in which case we need $m$ positive).
Then we'll need $$180=n+(n+m)+(n+2m)=3n+3m=3(n+m),$$ so $$60=n+m,$$ and so $$m=60-n.$$
Can you get the rest of the way?
